An overview of CMOS integrated switched-mode power amplifiers.
\r\n\tThis book is intended to provide a series of peer reviewed chapters that the guest editor believe will aid in increasing the quality of the research focus across the growing field of grain and seeds compound functionality research. Overall, the objective of this project is to serve as a reference book and as an excellent resource for students, researchers, and scientists interested and working in different functional aspects of grain and seed compounds, and particularly for the scientific community to encourage it to continue publishing their research findings on grain and seed and to provide basis for new research, and the area of sustainable crop production.
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Power amplifiers (PAs) determine much of the efficiency and linearity of transmitters in wireless communication systems, both on the base station side and in the handset device. With the move to third-generation (3G) communication systems as well as other systems such as Ultra-Wideband (UWB), a higher linearity is required due to envelope variations of the radio frequency (RF) signal. The traditional way of guaranteeing sufficient linearity is backing off the PA; however, this results in a significant drop in efficiency, and thus in reduced battery lifetime for the handheld device and increased cooling requirements for the base station. With the current energy costs, and increased density of base stations, this is fast becoming an important issue.
\n\t\t\tA second issue in current wireless communication systems is the requirement for a certain range of transmitter output power control, e.g. for 3G systems. Depending on the distance to the base station, a difference in handset output power in the range of tens of dB may occur. If the PA efficiency is peaking for maximum output power, and is reduced considerably for lower output power, the average efficiency of the transmitter calculated over its full output power range of operation will be low. Thus, efficiency improvement for lower output power is an important aspect in transmitter design.
\n\t\t\tMoreover, current wireless communication handsets require a multi-band/multi-standard approach, so that several communication standards are incorporated in one device. Ideally this would all be achieved by one PA, but current standard is that multiple PAs are used for multiple standards, in worst case each with its bulky, costly output filter.
\n\t\t\tIn order to address efficiency and linearity issues, different transmitter architectures have been proposed and implemented throughout the years, such as for instance Envelope Elimination and Restoration (EER) or Envelope Tracking (ET), varieties of polar transmission where the envelope and phase of the signal are processed separately. Also, different PA architectures have been used, such as Doherty and switched mode amplifiers, often complemented with linearity-improving measures such as digital predistortion or feedback.
\n\t\t\tWith the coming of age of handset production, cost effectiveness has driven wireless communication transceiver design to higher levels of integration. As many building blocks as possible are integrated on the same chip, and the use of external bulky filters is avoided if possible. CMOS technology has been the main choice for this development, due to the possible integration of digital, mixed-signal and analog circuits. However, CMOS was not suitable for PA design due to frequency, output power, efficiency and linearity requirements. Thus, the stand-alone PA has long been manufactured in III-V technologies or specialized technologies such as LDMOS.
\n\t\t\tIn recent years however, CMOS technology has evolved for radio frequencies in two ways: (1) Decreasing device dimensions have resulted in higher clocking frequencies, thus e.g. providing the opportunity for clocking speeds of several times the RF frequency; (2) The technology provides special RF properties such as thick top metal, allowing for e.g. integrated inductors or transformers with high quality factor. These two technology trends have enabled a higher level of transmitter integration. In combination with the use of switches, for which CMOS devices are extremely suitable, so-called digitally assisted RF transmitters have been designed, that is, transmitters where building blocks are switched on or off by means of digital control signals, or biasing settings are changed based on digital signals.
\n\t\t\tRecently transmitter design research has taken the next step: increasingly using digital techniques for the full transmitter. A fully integrated GSM radio has been presented with all-digital phase and amplitude signal paths, including an all-digital phase-locked loop. Other examples are a class-E switched mode PA with pulse-width and pulse-position modulation (PWPM) implemented with all-digital blocks, an array of power mixers, controlled by digital logic, and an array of digitally controlled cascode transconductance stages not unlike current-steering digital-to-analog converters, referred to as digital-to-RF conversion. However, efficiency over a wide power range is still a major concern, as will be shown.
\n\t\t\tIn this chapter an overview of switched-mode power amplifiers will be presented. This will be followed by an overview of transmitter architectures suitable for switched-mode transmitters; direct modulation as well as polar and Cartesian modulation will be described by looking at traditional architectures and recent developments, with focus on switched-mode implementations, resulting in a future outlook for integrated transmitter design for wireless communication.
\n\t\tGenerally a switched-mode (SM) amplifier consists of one or more transistors that are behaving as a switch, that is, having an on- and an off-stage, ideally without on-resistance and near-zero raise- and fall time. These conditions can be approximated by heavily overdriving the transistor input, and by operating the device at significantly lower frequencies than the device’s
Overdriving the transistor input, however, has certain consequences: the device will act non-linearly, and small-signal models are not always valid. Moreover, for wireless communication applications the difference between operating frequency and device unity gain frequency
It is only fairly recent that CMOS technology has come up as an alternative for integrated circuit power amplifier design, as CMOS previously was not suitable for PA design due to frequency, output power, efficiency and linearity requirements. Thus, stand-alone PAs have long been manufactured in III-V technologies such as GaAs or GaN, or specialized technologies such as LDMOS or SiGe bipolar junction transistors.
\n\t\t\t\tLargely driven by the drive for integrating more digital functionality on the same chip area, CMOS devices have continued to shrink in device dimensions, basically following Moore’s law. Accordingly, transistor
However, the trend of shrinking device dimension comes with certain distinct disadvantages for analog circuit design, and more specifically for PA design. Due to shrinking oxide thickness, the breakdown voltage of the devices is reduced, implying that supply voltages must be reduced for safe operation. This has implications for CMOS PAs, as the maximum output power, assuming load-line matching, is then given by
\n\t\t\t\tsuch that in a 50Ω system, and a supply voltage of 1V, the output power is limited to 10mW or 10dBm. Thus, impedance transformation must be used so that the amplifier sees a lower impedance. This is practically limited to 1-5Ω; Having such a low impedance makes the PA efficiency very sensitive to parasitic series resistance in the output network, because of conduction losses: A 0.1mΩ parasitic resistance in series with a load resistance of 1Ω gives a loss of 10%.
\n\t\t\t\tDue to these increasing technology limitations, in modern CMOS deep-submicron technologies special transistors are provided having a thicker gate oxide and thus allowing for higher supply voltage.
\n\t\t\tLooking at RF power amplifiers, we want to have an output signal at the frequency of interest – usually the fundamental frequency, sometimes a harmonic – but no disturbing output signals at other frequencies. In other words, some filtering must be performed in order to use a switch in a power amplifier.
\n\t\t\t\tThe ideal waveforms for a switched-mode (SM) transistor in a PA, assuming a broadband load, are shown in Figure 1. From this figure it can be seen that the voltage and current are ideally never non-zero simultaneously, thus no power is consumed, and ideally a 100% efficiency can be achieved. However, considerable power is generated at harmonic frequencies. Thus the maximum theoretical efficiency for this broadband SM PA is slightly larger than 80%, achieved at a 50% duty cycle.
\n\t\t\t\tIn order to reduce the power present in harmonic frequencies, a tuned amplifier can be used. This can be implemented in several ways. One way is by introducing harmonic shorts in parallel to
Another strategy is to have a resonance circuit in series with
Device and switching losses
\n\t\t\t\tAside from the harmonic losses discussed in the previous section, some other losses can be identified in a SM amplifier/transistor (El-Hamamsy, 1994). First of all, the transistor will
\n\t\t\t\tAn ideal switched-mode (SM) power amplifier, (a). Schematic, (b). Voltage and current waveforms.
suffer from non-idealities, of which one is a non-zero on resistance. This will cause a non-zero voltage drop and thus so-called conduction loss, resulting in reduced efficiency.
\n\t\t\t\tSecondly, the transistor will have non-zero rise- and fall times, potentially causing the current and voltage to be non-zero simultaneously. Also CMOS subthreshold current will contribute to this.
\n\t\t\t\tThirdly, dynamic losses due to charging and discharging of parasitic capacitors must be taken into account – the switching losses. These are proportional to the switching frequency
Other losses
\n\t\t\t\tExternal elements such as output networks may cause losses as well, for example a tuning or impedance transformation network consisting of on-chip or discrete passive elements. These inductors and capacitors will include parasitics such as capacitances or series resistances. These may cause power dissipation and thus reduce the amplifier efficiency.
\n\t\t\t\tA MOSFET is very suitable as a switch, toggling between the
where
The
Now that general technology issues have been discussed, SM amplifiers for radio frequencies will be addressed in this section, and an overview will be given of specific CMOS implementations.
\n\t\t\tIn amplifier theory, several different switched-mode types are established: the classes D, E and F (Cripps, 1999, Raab, 2001). They will briefly be addressed below, before looking into CMOS implementations in the next section.
\n\t\t\t\tClass-D
\n\t\t\t\tClass-D amplifiers use a double-switch structure, with a series resonance circuit (see Figure 2). The output current is alternatingly supplied by each switch, similar to a push-pull configuration. The simplest implementation for the two switches is an inverter. The maximum theoretical efficiency is 100%, with a square-wave voltage and a half-wave rectified sine wave current in each device. In that case the voltage contains only odd harmonics, and the current even harmonics.
\n\t\t\t\tSimplified schematic of a class-D amplifier, (a). A voltage-mode amplifier, (b). A current-mode amplifier.
This amplifier may also be implemented as current-mode (see Fig. 2b). Instead of having a series resonance circuit in series with the load, a parallel resonance circuit is then used at the output of the amplifier. In that case the current approximates a square-wave, containing odd harmonics, while the drain voltage for each device approximates a half-wave rectified sine wave. It has been shown that a high efficiency can be achieved, assuming the amplifier can be designed for Zero Voltage Switching (Long et al., 2002, Kobayashi et al., 2001).
\n\t\t\t\tClass-E
\n\t\t\t\tA class-E amplifier consists of a single switching device with a carefully tuned output network. The voltage derivative, close to the timing point when the device is switched off, is designed to be very small (so-called Zero Voltage Switching, ZVS) so that potential static losses are kept very low. Also for this amplifier the theoretical maximum efficiency is 100%.
\n\t\t\t\tOne of the characteristics of class-E is that large voltage peaks occur; thus, care must be taken to avoid high voltages across the CMOS device, as the breakdown voltage of CMOS devices is relatively low.
\n\t\t\t\tClass-F
\n\t\t\t\tA class-F amplifier is basically an amplifier with a current that approaches a half-wave rectified sine wave, and a voltage that approaches a maximally flat shape. Tuning a limited number of odd-order harmonics of the fundamental signal is used to achieve this. Two different structures are in use for class-F design, depending on which harmonics are seen at the drain: Regular class-F for odd-order harmonics, that is, the voltage is approximately maximally flat, and inverse class-F for even harmonics, i.e. a half-wave rectified sine wave-shaped drain voltage and a maximally flat shaped drain current (Raab, 2001). It must be noted that the inherent pulse shaping makes this amplifier less suitable for e.g. Pulse Width Modulated (PWM) input signals (Sjöland et al., 2009).
\n\t\t\t\tAll three amplifier classes depend to some extent on a frequency-selective output network. Thus, their operation cannot be considered broadband. Either they can only be used in a narrow, specific frequency range, or each amplifier’s behavior may show significant differences depending on the frequency of operation.
\n\t\t\t\tResearch is progressing into variable output networks, where digital control signals are used to e.g. change the frequency of operation, or reconfigurable PAs, as well as output networks allowing for concurrent multi-band operation (Colantonio et al., 2008). In such digitally assisted systems the use of CMOS technology, also for the PA, may lead to a higher level of integration. This will be addressed more extensively in the section on transmitter architectures.
\n\t\t\tBy the mid-1990s, the first publications on integrated CMOS PAs for RF appeared. These works initially focused on more or less linear amplifier structures such as class A, AB, B or C, but research has since then focused more on the switched-mode class-D, E and F, as higher clocking or switching speeds became available with improvements in CMOS technology.
\n\t\t\t\t\n\t\t\t\t\tSu and McFarland (1997) presented a 0.8µm CMOS SM amplifier consisting of four stages with the final stage in switched-mode. A Power-Added Efficiency (PAE) of 42% was achieved at 850MHz with a 2.5V supply, and largely off-chip input and output matching networks were used. Yoo and Huang (2001) presented a 0.25µm CMOS class-E PA, using a finite DC feed inductor to reduce the peak voltage over the device, as well as Common Gate (CG) switching instead of the more usual Common Source (CS) structure. These strategies allow for a higher supply voltage to be used, thus reducing the necessity for a low load impedance.
\n\t\t\t\t\n\t\t\t\t\tReynaert and Steyaert (2005) have presented a fully integrated 0.18µm CMOS class-E PA, consisting of three stages and including supply modulation to provide amplitude variation. A PAE of 34% was achieved for an output power of 23.8 dBm, using a supply voltage of 3.3 V and extra thick gate oxide for the final stage.
\n\t\t\t\tAs limited supply voltage is one of the major challenges in CMOS PA design, other strategies have been used to effectively add the output voltages, such as using a transformer to combine output power (Aoki et al., 2008, Haldi et al., 2008) or stacking devices, making sure that the voltage over each device stays below the maximum (Stauth & Sanders, 2008, Jeong et al., 2006). However, generally this slightly impairs the efficiency, counteracting the intended advantage of a higher supply voltage. Apart from voltage stacking, current combining has been implemented (Kavousian et al., 2008, Kousai & Hajimiri, 2009), as well as the switching in of several parallel stages (Walling et al., 2008). The latter two will be covered more in the section on transmitter architectures.
\n\t\t\t\tReference | \n\t\t\t\t\t\t\tClass | \n\t\t\t\t\t\t\tTechnology | \n\t\t\t\t\t\t\tSupply voltage | \n\t\t\t\t\t\t\tOutput power | \n\t\t\t\t\t\t\tEfficiency (PAE) | \n\t\t\t\t\t\t\tFrequency | \n\t\t\t\t\t\t
Su et al., 1997 | \n\t\t\t\t\t\t\tD | \n\t\t\t\t\t\t\t0.8µm CMOS | \n\t\t\t\t\t\t\t2.5 V | \n\t\t\t\t\t\t\t30 dBm | \n\t\t\t\t\t\t\t42% | \n\t\t\t\t\t\t\t850 MHz | \n\t\t\t\t\t\t
Tsai et al., 1999 | \n\t\t\t\t\t\t\tE | \n\t\t\t\t\t\t\t0.35µm CMOS | \n\t\t\t\t\t\t\t2.0 V | \n\t\t\t\t\t\t\t30 dBm | \n\t\t\t\t\t\t\t48% | \n\t\t\t\t\t\t\t1.9 GHz | \n\t\t\t\t\t\t
Yoo et al., 2000 | \n\t\t\t\t\t\t\tE | \n\t\t\t\t\t\t\t0.25µm CMOS | \n\t\t\t\t\t\t\t1.9 V | \n\t\t\t\t\t\t\t30 dBm | \n\t\t\t\t\t\t\t41 % | \n\t\t\t\t\t\t\t900 MHz | \n\t\t\t\t\t\t
Kuo et al., 2001 | \n\t\t\t\t\t\t\tF | \n\t\t\t\t\t\t\t0.2µm CMOS | \n\t\t\t\t\t\t\t3.0 V | \n\t\t\t\t\t\t\t32 dBm | \n\t\t\t\t\t\t\t43 % | \n\t\t\t\t\t\t\t900 MHz | \n\t\t\t\t\t\t
Sowlati et al., 2003 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 0.18µm CMOS | \n\t\t\t\t\t\t\t2.4 V | \n\t\t\t\t\t\t\t24 dBm | \n\t\t\t\t\t\t\t42 % | \n\t\t\t\t\t\t\t2.4 GHz | \n\t\t\t\t\t\t
Reynaert et al., 2005 | \n\t\t\t\t\t\t\tE | \n\t\t\t\t\t\t\t0.18µm CMOS | \n\t\t\t\t\t\t\t3.3 V | \n\t\t\t\t\t\t\t24 dBm | \n\t\t\t\t\t\t\t34 % | \n\t\t\t\t\t\t\t1.75 GHz | \n\t\t\t\t\t\t
Stauth et al., 2008 | \n\t\t\t\t\t\t\tD | \n\t\t\t\t\t\t\t90nm CMOS | \n\t\t\t\t\t\t\t2.0 V | \n\t\t\t\t\t\t\t20 dBm | \n\t\t\t\t\t\t\t38.5% | \n\t\t\t\t\t\t\t2.4 GHz | \n\t\t\t\t\t\t
An overview of CMOS integrated switched-mode power amplifiers.
As we have seen before, one of the basic requirements for power amplifiers in modern wireless communication systems is to accommodate envelope variations and to provide variable output power. Wireless communication standards have moved from constant-envelope, low- channel bandwidth to more complex signal shapes in order to increase data rates in limited bandwidth, resulting in variable envelope RF signals and larger channel bandwidths in the range of tens of MHz.
\n\t\t\tIn SM amplifiers output power variation can be achieved by varying the supply voltage, by varying the duty cycle of the signal, by varying the load, or by a combination of these. In this section some transmitter architectures will be discussed that adopt such strategies; only the strategy of varying the load impedance will not be addressed here.
\n\t\t\tOn the transmitter architecture level, one of the classical methods of varying the output power is based on polar modulation, where a baseband Cartesian signal
where
\n\t\t\t\tPolar modulation is recently gaining more and more interest due to its potential to maintain linearity while having a relatively high efficiency even for lower output power, thus improving the average efficiency over a wide output power range.
\n\t\t\t\tOne of the most well-known polar schemes is Envelope Elimination and Restoration (EER), brought to attention by Khan (Khan, 1952, Wang et al., 2006, Su & McFarland, 1998). The envelope is used to control the PA supply level, while the phase signal is upconverted to RF and transformed to a constant envelope signal, driving the PA input. Thus, a non-linear PA can be used. Su and McFarland (1998) have demonstrated a CMOS implementation of an EER system, including a delta-modulated supply, a limiter, and envelope detectors, driving a switched-mode PA, resulting in significant linearity and efficiency improvements.
\n\t\t\t\tSimplified representation of the Envelope Elimination and Restoration (EER) and Envelope Tracking (ET) transmitter architectures.
Envelope tracking (ET) describes a transmitter architecture where the Cartesian RF signal is amplified by means of a linear amplifier, with its supply controlled by the envelope of the signal (Hanington et al., 1999, Takahashi et al., 2008). One of the main advantages is that the bandwidth of the PA input signal is not expanded, but a linear amplifier generally has a lower efficiency than a SM amplifier. However, requirements on the envelope signal and timing are less stringent (Wang et al., 2006). So-called hybrid EER architectures have been demonstrated, where the ET linear amplifier is replaced by a SM amplifier, however, still driven by the full Cartesian RF signal (Wang et al., 2006).
\n\t\t\t\tBoth the EER, ET and hybrid EER depend on utilizing an efficient power supply modulator, that must be able to handle the bandwidth of the envelope signal. For this, a boost dc-dc converter, a Buck dc-dc converter, or a switched-mode low-frequency amplifier can be used, controlled by a Pulse Width Modulator (PWM), a Sigma-Delta modulator (ΣΔM) or a Delta modulator (ΔM) (Kitchen et al., 2007). Generally, independent of supply modulator type, a bulky low-pass filter must be used to filter out undesired signals such as noise or harmonics.
\n\t\t\tIf the duty cycle
assuming ideal frequency selection at the output. This can be used to accommodate the envelope and power variations in a polar transmitter, by changing the amplifier’s threshold voltage. Implementations exist with discrete steps as well as continuous change (Yang et al., 1999, Cijvat et al., 2008, Smely et al., 1998). A major advantage of these strategies is that no DC-DC converter is necessary; A disadvantage is that linearity may be worse compared to an amplifier where the supply voltage is changed, possibly resulting in tougher requirements for digital predistortion. Moreover, the efficiency drops rapidly at small duty cycles (Cijvat et al., 2008).
\n\t\t\t\t\n\t\t\t\t\tSmely et al. (1998) combined discrete supply voltage steps with changing the drain current of the output stage of a class-F stage by means of varying the GaAs MESFET gate voltage, depending on the amplitude of the input signal. Yang et al. (1999) focused on improving the efficiency of a class-A amplifier, by using variable bias to change the current in the output stage as well as changing the supply voltage.
\n\t\t\t\tVariable gate bias was used (Cijvat et al., 2008) for CMOS class-D amplifiers, with the goal of creating a PWM signal at the output of the amplifier. The proposed architecture uses the envelope signal to control the gate bias, and the RF signal is assumed to be sinusoidal, containing only the phase information.
\n\t\t\t\tFor this amplifier structure, loss mechanisms as discussed in section 2 cause a drop in drain efficiency for lower output powers. It is likely that switching and harmonic losses are significant; the amplifier switches as often as for full output power, thus having roughly the same switching loss, and the harmonic content of a PWM signal increases for duty cycles other than 0.5, thus increasing harmonic losses. As can be seen in Figure 4.b, the amplifier aimed for higher output power, having larger output devices and thus larger parasitic capacitances, reaches a lower maximum drain efficiency as a result.
\n\t\t\t\tAs was addressed by Sjöland et al. (2009), one of the challenges of polar modulation is the sharp notch in amplitude variation which causes fast amplitude variations that are difficult to track for a DC-DC converter with limited bandwidth. Thus, a combination of EER and Pulse Width Modulation is proposed. This is applied to the aforementioned 130 nm CMOS class-D inverters, and simulation results are presented in Figure 5.
\n\t\t\t\tIt can be seen from this figure that efficiency gains of EER and PWM combined are minimal in this case, compared to EER-only. Moreover, combining the two strategies will lead to greater transmitter complexity; the additional power that is required is not taken into account in the simulations. However, as was mentioned earlier, this solution may address the bandwidth limitations of EER.
\n\t\t\t\ta). Measured output power and efficiency of a 6 dBm 130nm CMOS class-D inverter chain, using gate bias variation to create a pulse width modulated inverter output voltage (
Simulated PA drain efficiency versus output power, combining EER modulation for high amplitudes and PWM for lower amplitudes. The voltage where EER takes over is varied; one curve shows results for a border value of 0.6V and the second curve for a border value of 0.9V.
A third method for varying the output power is so-called burst mode transmission. Effectively the RF signal is turned on and off by means of a bit stream. The envelope signal may be digitized e.g. by means of a or a Pulse Width Modulator (Jeon et al., 2005, Berland et al., 2006, Stauth & Sanders, 2008).
\n\t\t\t\tA burst-mode pulsed power oscillator to be used as a final stage in a transmitter was presented by Jeon et al. (2005). The oscillator is turned on and off by a PWM representation of the low-frequency envelope signal, thus resulting in the high-frequency RF signal multiplied by the PWM signal, appearing as bursts at the oscillator output. An isolator and bandpass filter are used to prevent reflected power to return into the oscillator and filter out undesired frequency components.
\n\t\t\t\t\n\t\t\t\t\tBerland et al. (2006) analyzed two varieties of using a one-bit signal to be multiplied with the slightly modified Cartesian signal. The one-bit signal was derived from the envelope signal by utilizing a Pulse Width Modulator and a Sigma-Delta Modulator, respectively. A high operating frequency of several GHz is, however, necessary to reach sufficient performance.
\n\t\t\t\tA polar modulator using a baseband ΣΔM and an RF Pulse Density Modulator (PDM) were used to drive a class-D amplifier with a 1-bit signal (Stauth & Sanders, 2008). This solution, basically all-digital, was implemented in 90nm CMOS and the cascade PA operated from a 2V supply. The PA performance can be seen in Table 1. The Bluetooth 2.1+EDR spectral mask was met for an output signal in the range of 10dBm, including a bandpass filter at the output.
\n\t\t\tIn analogy to current-steering Digital-to-Analog converters (Zhou & Yuan, 2003), a fourth strategy to control output power has recently gained attention, which is switching in parallel stages. One example is the work by Kavousian et al. (2008), where the low-frequency envelope of the polar signal was transformed into a thermometer code used to switch on and off unit stages, while the constant-envelope RF phase signal drives the input of each stage. The authors refer to this as digital-to-RF conversion.
\n\t\t\t\t\n\t\t\t\t\tShameli et al. (2008) used 6 control bits to both switch in a number of parallel output stages and at the same time change the supply voltage with a ΣΔ modulator. A 62 dB power control range was achieved, as well as a 27.8dBm maximum output power and an average WCDMA efficiency of 26.5%.
\n\t\t\t\tCurrent summing was also used by Kousai and Hajimiri (2009), utilizing 16 parallel power mixers and a transformer at the output. The phase information modulates the high-frequency digital LO signal. Linearization could be chosen to be analog, by sensing and feeding back the signal level for each mixer core, or digital, by using a thermometer code for the envelope signal, switching on and off mixer cores. Both the baseband and the LO signal where controlled digitally with a number of bits. A 16-QAM (Quadrature Amplitude Modulation) signal at 1.8 GHz and a symbol rate of 4 MSym/s was reproduced with an output power of 26 dBm, a PAE of 19% and an EVM (Error Vector Magnitude) of 4.9%.
\n\t\t\t\t\n\t\t\t\t\tPresti et al. (2009) used 7-bit thermometer + 3 bit binary weighted current summing combined with analog input power control for low-power levels. Relative broadband operation, 800-2000 MHz, and a 70dB power control range is achieved. With Digital Pre-Distortion (DPD) both WCDMA, EDGE and WiMAX specifications are met.
\n\t\t\t\tIn these architectures no supply voltage modulator is used. Sufficient resolution to achieve a high linearity or amplitude accuracy is achieved by increasing the number of parallel stages. However, the efficiency of these current-summing amplifiers follows a class-B curve (Presti et al., 2009):
\n\t\t\t\t\n\t\t\t\t\tWalling et al. (2008) used control bits to generate a suitable Pulse Width/Pulse Position (PWPM) signal, which was then provided to four class-E quasi-differential stages. In a 65nm technology, a maximum output power of 28.6 dBm and PAE of 28.5% is achieved at 2.2 GHz with the output stage using a supply voltage of 2.5 V. For a 192kHz symbol rate, non-constant envelope π/4-DQPSK (Differential Quadrature Phase Shift Keying) modulated signal, an output power of 27 dBm is achieved with an EVM of 4.6%.
\n\t\t\tA third strategy to process the signal is to directly modulate the RF signal into the SM amplifier. For instance, a Pulse Width/Pulse Position modulator (PWPM) or a Sigma-Delta (ΣΔ) modulator can be used (Nielsen & Larsen, 2008, Wagh & Midya, 1999). This is depicted in Figure 6. A major disadvantage however is that generally a high sampling or operating frequency is necessary, typically at least 4
Direct modulation of the RF signal by means of Sigma-Delta (ΣΔ) or Pulse Width Modulation (PWM).
\n\t\t\t\t\tWagh and Midya (1999) presented the concept of Pulse Width Modulation for RF. Nielsen and Larsen (2008), utilizing GaAs technology, used a feedback circuit and a comparator to generate an RF PWM signal. The signal’s adjacent channel power ratio stayed well below the UMTS spectrum mask, allowing for some non-linearity from a subsequent PA.
\n\t\t\t\tDirect modulation was also proposed by Jayaraman et al. (1998), utilizing a bandpass ΣΔ modulator, simulated with GaAs HBT technology. Discussions on efficiency were presented, and it was indicated that the linearity demands were moved from the PA to the ΣΔM.
\n\t\t\tEven though polar modulation has some distinct efficiency advantages, as an alternative Cartesian modulation may be used, that is, the
\n\t\t\t\t\tBassoo et al. (2009) have proposed a combination of Cartesian and polar modulation, where the SMPA input signal is a SD modulated Cartesian signal divided by the amplitude signal, which may be more or less bandlimited (see Figure 7). Analysis showed that the envelope signal can be limited to 75% of the channel bandwidth without impairing the efficiency, still keeping OFDM clipping limited and EVM very low. Thus, a combination of EER and PWPM can be used to have a high efficiency over a wide range of output power while avoiding the bandwidth expansion of polar modulation.
\n\t\t\tSimplified architecture presented in
Simulations have been performed on a 130nm CMOS class-D switched-mode amplifier, in order to compare the drain efficiency versus output power of the different architectures that have been discussed in the previous sections, such as Envelope Elimination and Restoration (EER), Envelope Tracking (ET), and Pulse Width Modulation by Variable Gate Bias (PWMVGB). Moreover, hypothetical curves for class-A and class-B operation have been drawn (see Figure 8), with the peak efficiency as starting point. Class-A represents linear amplifier operation while class-B can be said to represent current-summing architectures.
\n\t\t\t\tNot unexpectedly the EER and ET architectures perform best, showing the highest efficiency for lower output power ranges. It may thus be concluded that the use of supply modulation is desirable for high average efficiencies. However, it can also be seen that efficiency remains a challenging aspect, especially taking into account numerous other requirements such as linearity, channel bandwidth, multi-mode/multi-standard operation and output power control range.
\n\t\t\tIt is only fairly recent that CMOS technology has become a competitive alternative for integrated circuit power amplifier design for wireless communication handsets, as CMOS previously was not suitable for PA design due to frequency, output power, efficiency and linearity requirements. Thus, stand-alone PAs have long been manufactured in specialized technologies. Nowadays however CMOS has evolved to operating frequencies far into the GHz range, and many of the limitations, such as efficiency when used as linear amplification element, can be compensated by more digital control. Thus, a higher level of integration and more complex transmitter design result. However, the trend in CMOS technology development is to reduce device dimensions and as a consequence breakdown voltage. This complicates CMOS power amplifier design.
\n\t\t\tSimulated drain efficiency for a CMOS class-D amplifier in different architectures, such as Envelope Elimination and Restoration (EER), Envelope Tracking (ET), and Pulse Width Modulation by Variable Gate Bias (PWMVGB). Class-A and class-B curves serve only as an illustration. The amplifier operated on a 1.2V supply and the input signal had a frequency of 2 GHz. (a). The output power (x-axis) represented in dBm, (b). The output power in mW.
Transmitter architectures using polar signals have gained in popularity, as splitting the Cartesian signal into a low-frequency envelope signal and a high-frequency phase signal provides excellent opportunity for efficiency improvements because a non-linear power amplifier can be used. A number of different polar architecture implementations exist, both digital and analog. However, signal bandwidth and supply requirements are challenging aspects of such designs. Other strategies have thus been used to avoid supply voltage modulation, such as switched control of the supply voltage or variable gate bias. Moreover, direct RF modulation can be used, implemented as a sigma-delta or pulse width modulator at high operating frequency. Recently, design strategies such as current steering have gained interest for use in PA and transmitter design. Digital control bits are used to generate a scaled output current, providing a high output power without straining the devices.
\n\t\t\tHowever, efficiency over a wide range of output power is still a challenging aspect of transmitter design, especially if other requirements such as linearity, power control, multi-mode/multi-band operation and channel bandwidth must be fulfilled simultaneously.
\n\t\t\tAs CMOS technologies continue to develop to dimensions well below 65nm, special devices suitable for high supply voltage will likely continue to be provided, for example using high-K metal gate material. Such devices can be used on the same chip as digital circuits with clocking speeds of several GHz. Moreover, other substrate types may be used more extensively, such as Silicon-on-Isolator substrates. As they are less lossy, this may provide efficiency improvements.
\n\t\t\t\tOn the other hand, performance requirements will continue to rise with the development and maturing of wireless communication systems, especially because of the desire to cover more and more standards in one handset (multi-mode/multi-standard operation). Digital control may be used to accommodate greater flexibility, reconfigurability and on-chip calibration in transmitter design. Moreover, techniques may be used to increase the adaptivity of components such as antennas, duplexers, filters and matching networks.
\n\t\t\t\tCMOS will continue to expand into the millimeter-wave range, with operating frequencies beyond 60 GHz. However, other technology developments may play an important role in future integrated circuit design for wireless communication, such as integrated RF MEMS (microelectromechanical systems). Also devices such as carbon nanotubes may be used for wireless applications. But such technologies have some way to go until they reach the level of integration that current CMOS technology has.
\n\t\t\tThermal management becomes increasingly important and challenging as the increase of power/heat density is taking place in many engineering applications, products, and industrial sectors. One example is the electronics industry. Advances in semiconductor manufacturing technology create more compact integrated circuits for electric devices. The latest Fin Field Effect Transistor (FinFET) technology contributes to the reduction of fabrication node from 22 nm in the year of 2012 to the current 10 nm, and even to 5 nm in 2021. Using a 10 nm FinFET manufacturing process, Apple A11 chip could contain 4.3 billion transistors on a die of ~87 mm2, which is 30% smaller than the last version A10. In addition, thermal design power of electric chips, the maximum amount of heat removal from the electric chips, shows an increasing trend. As heat power density continues to grow, heat removal, also referred to as thermal management, is important for maintaining the temperature to meet material and safety constraints. In turn, the development and maintenance of electric devices rely on how effectively the heat is dissipated from the devices. The choice of cooling technology is a complicated systems work in high-power electronic, not only for fitting in the heat removal requirement from low power density to high power density, but also for considering the cooling efficiency, power load, overall power consumption of the cooling subsystem, and the cost of cooling infrastructure. This chapter focuses on fundamental heat removal capacities of cooling technology.
\nDifferent cooling technologies vary in their heat removal capacities, which are summarized in Figure 1. For low heat flux removal requirement, air-cooling, which removes the heat from the hot surface by airflow, is widely applied. The cooling performance can be enhanced by expanding the surface area or increasing the flow of air over the surface. The first approach is known as air free convection, while the second approach is air-forced convection. In comparison with free convection, the fluid motion in forced convection is generated by external source, for enhancing the local convection. In computers, cooling fins are added to heat sink for expanding the surface area, while a fan is attached to the cooling fins to enhance air convection. Heat flux by forced air convection can reach ~35 W/cm2 while only ~15 W/cm2 by free air convection (see Figure 1). Due to the increase of power density, many micro-electronic and power electronic devices now are in the range of heat flux beyond the air cooling capacity. Effective liquid cooling solutions are needed for thermal management of the high-heat-flux devices.
\nHeat removal capacity by applying different cooling technologies that is characterized by two parameters: Highest heat flux and heat transfer coefficient [
Spray cooling is one effective solution, which has the huge potential in handling the high heat fluxes in high-power electronics such as supercomputer, lasers, and radars. Spray cooling has several advantages over other cooling techniques. In comparison with air-cooling and jet impingement cooling, spray cooling owns a high heat flux removal capacity. Spray cooling can transfer heat in excess of 100 W/cm2 using fluorinerts and more than 1000 W/cm2 using water (see Figure 1). Due to high heat flux removal capacity, spray cooling allows precise temperature control with low fluid inventory [5]. Besides, spray cooling has uniform cooling temperature distribution over the entire spray-covered surface. This is because the entire spray-cooled area is receiving fresh liquid coolant droplets. For jet impingement cooling, the coolant flows radially outwards from the impingement spot. The radial flow has non-uniform temperature, and the largest subcooling and the optimal local cooling occur at the stagnation point. The non-uniform cooling results in non-uniform surface temperature in the cooling area, which could be significant for high heat fluxes.
\nHowever, there are still some barriers for applying spray cooling for engineering applications. Significant pumping power is needed to achieve large pressure drop through spray nozzle to produce fine spray, but the low cost is first priority in commercial application of cooling technologies. Another fact that the design and fabrication of spray nozzle do not follow the identical industry standard makes the unpredictable spray characterization. Hence, it is hard to get a universal correlation of spray characterization to cooling performance, which also limits the implementation of spray cooling. Additionally, in comparison with the jet nozzle, nozzle orifice through the spray coolant is even smaller, increasing the possibility of orifice clogging and the occurrence of the dry-out area on the heated surface [6]. In spite of these barriers, spray cooling is still a popular cooling technology and many successful applications were reported for supercomputer (CRAY X-1) [7], laser diode laser arrays [8], microwave source components [9] and NASA’s reduced gravity aircraft [10].
\nIn spray cooling, liquid coolant is emitted from a pressurized nozzle and breaks up into numerous droplets. The small droplets land on the cooled surface, where the flow of droplets becomes a thin liquid film radially flowing on the surface (see Figure 2a). The cooling is achieved through the convection heat transfer from the cooled surface to the film flow being impacted by continuous flow of droplets, nucleate boiling on the cooled surface, liquid conduction inside the film flow, and interfacial evaporation from the liquid film to the surrounding air. Spray cooling provides uniform cooling that can handle high heat fluxes in both single phase and two phases. The cooling performance as a function of spray characterization, flow conditions, surface conditions, and nozzle positioning was widely discussed in past decades. These studies focused on the relationship between the spray cooling performance and the entire spray flow. However, in these spray-level studies, the understanding of cooling mechanism of spray droplets is missing. At the droplet level, the impact conditions are classified into a few categories (see Figure 2b): (a) impact of single droplet on dry surface appearing in nucleate boiling, transition boiling and film boiling, (b) impact of single droplet on stationary film where the radial velocity of the film is close to zero, such as stagnation zone, (c) impact of single droplet on radially flowing film and (d) impact of droplet burst on flowing film (droplet groups that frequently impact the surface). Although spray impingement cannot be simply considered as the superposition of single droplets due to the interaction of the neighboring droplets [11], the study of local cooling performance at droplet level is still significant to the understanding of spray cooling mechanism, especially for the condition of the local film dominated by the droplet flow. Therefore, the research outcomes of spray cooling are reviewed from two aspects: the spray level and the droplet level.
\nSpray cooling mechanism at the entire spray level (a) and droplet level (b).
Spray cooling can handle high heat flux in the constrictive space of electronic package when comparing to air-cooling, pool cooling, and jet cooling. This is because numerous fresh droplets generated by spray nozzle randomly affect the entire surface, and directly transfer the heat from surface to the coolant. The difference of fluid dynamics between spray impact and other cooling methods is a key factor affecting the mechanism of local heat transfer and resulting in different cooling performance. The first step of studying spray-cooling mechanism is to observe what happened on the heated surface. Numerous fundamental studies have been conducted theoretically and experimentally, which focus on the key parameters affecting impact dynamics and the relevant heat transfer mechanism. There are four aspects that have been demonstrated to significantly affect cooling performance, including spray characterization, nozzle positioning, phase change and enhanced surface [5, 6, 9].
\nSince the earliest study on spray cooling by Toda [12, 13], many researchers put effort on spray characterization, the relevant cooling performance and the critical heat flux (CHF) in spray cooling. Spray characterization mainly involves droplet size, impact velocity, droplet flux, and volumetric flux. However, in experimental studies it is difficult to change only one parameter and isolate the remaining parameters. For example, on the cooled surface the increase of flow rate of coolant spray is accompanied with the increase of impact velocity and volumetric flux with a constant impact area. That is reason that the conclusions made on the dominant impact parameter are not consistent in previous studies of spray cooling.
\nChen et al. [14] studied effects of three spray parameters of droplet size, droplet velocity and droplet flux on CHF. By adjusting spray nozzles, operating pressures, and spray distance between the nozzle exit and the heater surface, the effect of one spray parameter was studied while the others were kept constant. It was found that the mean droplet velocity is the most dominant parameter affecting CHF followed by the mean droplet flux, while the Sauter mean droplet diameter (\n
In single-phase spray cooling, spray droplets land on a radially flowing film. Some researchers studied the property of the flowing film and its relation to spray cooling performance. Pautsch and Shedd [17] used a non-intrusive optical technique to measure the local film thickness generated by sprays. The film thickness was found to remain constant when the heat transfer mechanism was dominated by single-phase convection. Beyond the spray impact area, the dry-out phenomena appear even when the CHF is not reached. In the nucleate boiling regime, Horacek et al. [18, 19] measured the dry-out area, which was characterized by the three-phase contact line length, and measured using a Total Internal Reflectance technique. The wall heat flux was found to correlate very well with the contact line length. This contact line heat transfer mechanism was summarized by Kim [20] as one of main heat transfer mechanisms in the two-phase regime.
\nCooling performance can be influenced by changing the spray positioning. There are two significant positioning parameters in the study of spray cooling (see Figure 3): nozzle-surface distance \n
(a) The 2D geometry is on the central plane (z-x plane) of the cone perpendicular to the impacted surface (x-y plane). The positioning of the nozzle is determined by inclination angle
Some researchers focus on the effects of spray inclination on heat transfer performance. The impact area is circular for normal impact \n
There are three reasons addressed for contradictory conclusion of spray inclination. One is regarding the different nozzle positioning. As illustrated in Figure 3, two key parameters, spray distance and inclination angle, determine the nozzle positioning. However, at a certain inclination angle some studies [23] applied the constant spray distance, while others [4, 24, 25] adjusted the distance for the constant impact length. Another reason is related to the assumption of one dimensional steady-state conduction through the neck of cartridge heater for the surface heat flux calculation. Inclined spray impact causes considerable temperature difference on the cooled surface (see Figure 4). Hence, the radial conduction should be taken into account for inclined spray cooling. The last reason is from the surface temperature measurement location. Different radial locations provide different temperature measurement due to significant temperature difference in inclined spray cooling.
\nLocal surface temperature distribution for normal impact (a1) and inclination affect with
To obtain surface temperature distribution in inclined spray, some researchers investigated local heat transfer by replacing cartridge heater with sputter-coated thin film heater, which enables infrared thermography for temperature measurement [21, 27, 28]. All of these studies found significant temperature difference on cooled surface for inclined spray cooling (one example in Figure 4b1). Gao and Li [27] compared the droplet impact velocity and heat transfer coefficient distribution along centerline for normal impact and inclined spray impact (see Figure 4a2 and b2). The impact velocity was captured by a Stereo-Particle Imaging Velocimetry system. The trend line of heat transfer coefficient and droplet velocity shows clear correlation. For both cases, the locations of maximum droplet velocity coincide with the locations of the highest heat transfer coefficient. The further study by Gao and Li [21] indicated the global cooling shows slight diminishment for small inclination angle and enhancement for large inclination angles. On the central plane of the spray cone, the enhancement and diminishment of the local cooling performance are in general agreement with the increase and decrease of the spray flux. Thin film heater is not reliable for the surface temperature greater than boiling point, and experiments are tested in single-phase region. This is the limitation of thin film heater, and the robust heater for boiling test is needed for future study.
\nSimilar to pool boiling curve, the heat transfer curve of spray cooling can be separated to four regimes: single phase regime, nucleate boiling regime, transition boiling regime and film boiling regime [12, 13]. In the single phase regime, the heat flux linearly increases with increasing surface temperature difference between heater surface and coolant. Forced convection by radially moving film and evaporation on unsteady interface of thin film layer, play dominant roles in single-phase regime [29]. In the nucleate boiling regime, bubbles begin to repeatedly occur at nucleation sites on the heated surface, and the heat flux sharply increases as compared to single-phase cooling. Once the nucleation sites cover the heated surface completely, average heat flux will reach a peak value, which is defined as Critical Heat Flux (CHF).
\nOnce reaching the CHF and coming to the transition boiling (decreasing region in the boiling curve), the efficiency of heat transfer on the heating surface significantly decreases. Liquid coolant absorbs heat from the surface and forms the vapor blanket, so the surrounding liquids are hard to get to the heater surface. That is the reason for the sharp decrease of heat flux in this regime. In the film, boiling regime an interesting phenomenon is an increasing trend of heat flux. Massive heat is generated from the heated surface and radiation heat transfer becomes a key heat transfer mechanism between the heated surface and the liquid, so the heat flux tends to increase from the Leidenfrost point. Considering the safety limit and fast implementation of electronic cooling, researchers’ attention is paid to the theoretical correlation in single phase regime and nucleation boiling regime.
\nIn the single phase regime, Rybicki and Mudawar [4] proposed the correlation for dielectric PF-5050 spray, which is
\nHere \n
The correlation has an accuracy of ±7.3% for varied pressure drops. Heieh and Tien [29] studied R-134a spray cooling, and correlated the Nusselt number to the Weber number, size distribution and sensible heat effects in the single phase regime, which is
\nIn the nucleate boiling regime of spray cooling, the heat flux increases with the surface temperature faster than that in single-phase regime. Yang et al. [31] proposed two reasons. In nucleation, boiling bubble appears and grows on nucleation sites as the liquid coolant changes to the vapor. During the phase change, a larger amount of heat is removed from the heated surface, resulting in a temperature drop on nucleation sites. The other reason is attributed to the influence of secondary nucleation and evaporation on the heat flux enhancement [32]. When the numerous droplets impinge on heated surface, air is entrained into the liquid film, forming an air layer underneath the droplets. The air layer reaches the liquid-covered surface and finally breaks up into many tiny gas nuclei, which serve as secondary nucleation sites. Hence, the number of secondary nucleation sites is proportional to the droplet flux across the surface, which was proved in Yang’s experiments [33]. Using water as coolant liquid, Mudawar and Valentine [16] proposed the CHF correlation with respect to the local volumetric flux \n
In another study by Estes and Mudawar [34], a universal CHF correlation was constructed for spray cooling by using Fluorinerts FC-72 and FC-87 as well as the water.
\nEnhancing spray cooling by changing the surface structure is one effective and low-cost approach, which benefits from optimal liquid management and enhancement of local cooling efficiency. According to the structure size, enhanced surface is classified into four categories: mini-structured surface, micro-structured surface, nano-structured surface, and hybrid-structured surface. Most of early studies of spray cooling have been conducted on flat surfaces. A few of them focus on the effects of surface roughness on cooling enhancement. Pais et al. [35] fabricated three rough surfaces using polishing grit with the size range of 0.3–22 μm and examined the roughness influence on heat removal capabilities. Tests showed that as the surface roughness decreases the CHF increases. CHF is up to 1200 W/cm2 on the surface by polishing grit of 0.3 μm while only 1000 W/cm2 on the surface by 22 μm grit. This is because the large surface roughness implies a thicker film thickness, leading to the later bubble breakup and departure, the impeding of vapor escape, the increased resistance to heat flux through evaporation on film surface, and the dampening of droplet impingement.
\nMini-textured surfaces feature structure size above 1 mm, and the structure types of cubic pin fins, pyramids, and straight fins and so on (see Figure 5a). Silk et al. [23] observed that addition of finned structure to cooled surface decreases the convective thermal resistance, and increases the convection heat transfer relative to the flat surface, since the total wetted surface area is larger on the enhanced surface. Although the cubic pin fins and straight fins have the same wetted surface area, cooling performance of straight fins surface exceeds that of the cubic pin fins surface. This is attributed to liquid management on the heated surface and cooling efficiency on the wetted surface area. Xie et al. [39] indicated that the fin arrangement is a dominant factor in enhancing heat transfer rather than the wetted surface area. The improper fin arrangement causes the thick and slow moving liquid film and thus worsens the local cooling performance. This point of view needs further validation by measuring the change of local surface temperature.
\n(a) Millimetric structured surface [
Micro/nano or hybrid structured surfaces have been attracted huge attention to spray cooling as micro fabrication technology advances new micro-/nano-engineered surface in the last decade (see Figure 5b, c, d). The experimental studies [36, 39, 40, 41] applied micro-textured surfaces with surface feature size from 25 to 480 μm, which is close to liquid film thickness but larger than average droplet size. Micro-textured surfaces showed slight effect on heat transfer enhancement in the flooded region, but greatly enhancing cooling performance in the thin film and partial dry-out regions as compared to the flat surface. The study by Zhang et al. [37] showed that nanostructured surface has better cooling performance since the contact angle is smallest on the nanostructured surface as compared to micro-structured surfaces and flat surfaces. Recently, Chen et al. [38] developed a hybrid micro/nano structured surface by growing the ZnO nanowire arrays on the top of etched micro-structured silicon wafer. Test results showed that cooling performance of hybrid surface is better than the micro-structured surface in boiling regime because of its great wetting capacity and reduction in dry-out surface area. If comparing performance of nanostructured surface [37] and hybrid surface [38], there is no significant difference in heat flux enhancement relative to the smooth surface.
\nThe impact dynamics during spray cooling is complicated as it involves many liquid phenomena, such as spreading, receding, splashing, droplet collision, generation of stationary film and radially flowing film, and liquid flooding. All of these impact phenomena result from the interaction of droplet flow and film flow on the impact surface. Droplet flow includes three types: single droplet, droplet train (continuous droplets formed from jet breakup), and droplet burst (portion of droplet train selected at a certain frequency). Similarly, film flow conditions involve dry surface (no film), stationary film, radially flowing film, or their combination on the cooling surface (see Figure 6).
\nSingle water droplets with same velocity and diameter (
The droplet and film flow conditions are two flow parameters directly determining the heat transfer mechanism of spray cooling. Coolant droplets bring significant temperature difference between the expanding droplet flow and flowing film, which contributes to the reduction of thermal resistance inside the film layer and enhancement of heat transfer from the heated surface to the flowing flow. Fluid dynamics on the impact surface is responsible for the local convection heat transfer. The fast flowing film transfers more heat to downstream. Thin film thickness reduces the thermal boundary layer and encourages evaporation from the liquid interface. Therefore, the fluid dynamics study of droplet affecting film enables us to get insight into thermal results of droplet impact on the film-cooled hot surface, and further understand spray cooling performance. The relevant literature is reviewed based on the droplet flow condition: single droplet impact, droplet train impact, and droplet burst impact.
\nThe dry surface usually appears in two-phase spray cooling, which is shown by the change of contact line length. The researchers reported that the critical heat flux in spray cooling is achieved at the greatest contact line length. On dry surface, droplet impact dynamics on droplet-covered surface area is essential to local cooling performance. The process of a liquid droplet impact was divided by Rioboo et al. [43] into five successive phases: kinematic, spreading, relaxation, wetting, and equilibrium. Most research work has been focused on spreading and relaxation. In the spreading phase, contact line expands radially until reaching a maximum spreading, which is determined by droplet initial diameter, impact velocity, surface tension, viscosity, and wettability of the solid surface (Li et al. [44]). The maximum spread diameter is of critical importance in spreading phase. Clanet et al. [45] found that on a super-hydrophobic surface the maximal spread is significantly dependent on the viscosity of liquid droplets and scales as a function of Weber number~We1/4. van Dam and Clerc [46] found a significant difference of maximum spread between substrates with small and large contact angles, showing the significant influence of wettability in the later stage of impact. A lower air pressure was found to suppress the droplet spreading, leading to a smaller maximum spread [47].
\nSome analytical models were proposed to predict impact process, most of which were based on the energy conservation of the impact droplet. Chandra and Avedisian [48] developed an empirical correlation of viscous dissipation, including estimated spreading time, simplified dissipation function, and estimated volume of viscous dissipation. Gao and Li [49] proposed a theoretical model based on the actual dynamic shape of the droplet that could successfully predict the maximum spreading diameter and receding diameter during the recoiling process. Some of the researchers put efforts on the investigation of splash using varied dry surfaces. Surface roughness and textures were demonstrated to influence the splash limit [50, 51]. Droplet impact on a moving surface was found to show different splash and non-splash phenomena as compared to stationary surfaces [52]. Previous studies on splash threshold under different surface conditions are summarized in Table 1.
\nSurface conditions | \nThreshold parameter | \nCritical value | \nReferences | \n
---|---|---|---|
Dry surface | \n( | \n57.7 | \nMundo et al. [50] | \n
0.8458 | \nVander Wal et al. [53] | \n||
Moving dry surface | \n5700 | \nBird et al. [52] | \n|
Stationary liquid film | \n( | \n2100 | \nCossali et al. [54] | \n
63 | \nVander Wal et al. [53] | \n||
Flowing liquid film | \n3378 | \nGao and Li [42] | \n
Summary of splash thresholds under different surface conditions [42].
On heated dry surface, Bernardin et al. [55] mapped the boiling curve of droplet impact cooling as the same as the spray cooling. In the regime of single-phase liquid cooling, Pasandideh-Fard et al. [56] observed that increasing impact velocity would enhance heat flux around the impact area. This is because the raising droplet velocity promotes droplet spreading, thus increasing the wetted area on the heated substrate. However, increasing droplet impact velocity slightly enhances heat flux at the impact point. Batzdorf et al. [57] proposed a theoretical mode to predict the heat transfer rate during the droplet impact. The theoretical prediction is more accurate when the liquid Prandtal number \n
On superheated surface with temperature over 200°C, Tran et al. [58] found three significant phenomena after droplet impact: contact boiling (droplet contacts with the surface), film boiling (vapor layer formed underneath the droplet), and spray film boiling (vapor layer and tiny droplets ejected upward) (see Figure 7a). Their experiments showed that the maximum spreading of a droplet impact follows a universal scaling with the Weber number (~We2/5), which is steeper than that on nonheated surface (~We1/4) [45]. The steeper curve on heated surface results from a driving mechanism, which is caused by the evaporating vapor radially expanding and pushing liquid outward. Staat et al. [59] indicated that the Leidenfrost transition temperature shows little dependence on the Weber number of affecting droplet, but the transition to splashing shows a strong dependence on the surface temperature. Adera et al. [60] reported the formation of non-wetting droplets on a super-hydrophilic micro-structured surface by slightly heating the surface above the saturation temperature of the droplet fluid, which is contributed by the increased thermal conductivity and decreased vapor permeability of the structured region. In experimental study of Jung et al. [61], the transient temperature distribution during droplet spread was detected using infrared thermography. In contact boiling, the droplet coolant contacts the surface and the maximum heat flux is quick to reach at early impact stage ~2 ms at impact point. In film boiling, non-wetting surface appears at the early impact, and the maximum heat flux is even lower than that in contact boiling due to the existence of vapor layer underneath the droplet. On heated surface, the study of simultaneous impact of multiple droplets is few, which needs further discussion of droplet collision influence on contact line and local evaporation. This benefits the understanding of two-phase spray cooling and optimization of cooling efficiency.
\n(a) Phase diagram of water droplet impact on a superheated surface [
Stationary film occurs in the center of normal spray impact, or locates where the spray nozzle axis insects with the impact surface in inclined spray (see Figure 2). On a stationary film, most researchers focused on spread process and splash formation mechanism after impact. Yarin and Weiss [62] developed a quasi-one-dimensional model, which predicts the existence of a kinematic discontinuity in the velocity and film thickness distribution. The discontinuity corresponds to the emergence of an uprising liquid sheet. Roisman and Tropea [63] generalized Yarin’s theory for the case of arbitrary velocity vectors in the liquid films both inside and outside the crown. Yarin and Weiss [62] experimentally found the crown radius from the impact center could be expressed as a function of the non-dimensional spreading time. Two empirical parameters existing in their model was given by the later study of Cossali et al. [64]. Droplet impact on a stationary film may or may not result in the splash. Finding the threshold condition for splash impact has been the focus of a few experimental studies. Cossali et al. [64] tested drops of various mixtures of water and glycerol affecting a thin liquid film and proposed an empirical parameter for predicting the occurrence of splash impact. For thick films, Cossali et al. [54] and Rioboo et al. [65] found a critical value of the threshold parameter, i.e. \n
The interaction between droplet flow and film flow is fundamental fluid dynamics in single-phase spray cooling or nucleate boiling (see Figure 2b). Impact dynamics was addressed in some researches. Alghoul et al. [66] presented an experimental investigation of a liquid droplet affecting onto horizontal moving liquid films. An asymmetrical crown shape was observed due to the effect of the moving film. Che et al. [67] demonstrated the on inclined falling flow asymmetrical crown shape is also formed after droplet impact. Gao and Li [42] further analyzed the early evolvement of droplet impact based on experiments and theoretical model (see Figure 6c). Once droplet lands on the film, the droplet flow quickly spreads and pushes the liquid outwards, causing the uprising liquid sheets. However, crown sheet is asymmetric owing to the collision mechanism on crown base. At the early stage of droplet impact, the direction of spreading flow is opposite to that of film flow at the upstream of impact point, while their direction is the same at the downstream. Uprising crown sheet may splash, which is dependent of the instability of the sheet rim. The stretching rate of crown sheet is a key factor influencing the rim instability. Analysis was conducted to derive equation of stretching rate, finding that the highest stretching rate appears at the location which droplet spreading flow is right opposite to the film flow, and the location is also the most probable location of splash. The value of splash threshold was provided to estimate whether splash occurs or not. The secondary droplets from splash fly away from the cooled surface, which do not contribute to the cooling performance. In other words, suppression of splash occurrence should benefit cooling enhancement.
\nThe late study of Gao and Li [68, 69] further observed the whole development of droplet impact on flowing film, and demonstrated its relation to the local cooling. The impact process is observed by high-speed video, showing two states: spreading state, replacing state. In spreading state, the droplet flow spreads and gradually slows down until reaching the maximum spread. After that, the droplet flow is pushed towards the downstream and eventually replaced by the film flow. The measured temperature also shows two stages: response stage when the temperature quickly decreases, and recovery stage in which the temperature recovers to the steady state. An enhancement factor was proposed to indicate convection enhancement relative to the steady-state cooling. The peak enhancement is used to consider enhancement influence of impact velocity, droplet size and film flow rate, which is proportional to the square root of the ratio of the droplet flow rate to the film flow rate~\n
One possible phenomenon in spray cooling is that fresh droplets continuously impact the surface at a certain frequency. The droplet flow is defined as the droplet train flow. The fluid dynamics behind this is the interaction of continuous droplet train flow with the flowing film formed on the heated surface. To investigate heat transfer of spray cooling from this aspect, a few studies have been conducted on the heat transfer of continuous droplet train impinging on hot surfaces. Qiu et al. [70] demonstrated surface temperature influence on the impact dynamics. Prior to the steady state, the droplet film spreads on the heated surface, and the surface temperature enhances the spreading rate of the flowing film when the surface temperature is over the boiling point. With the increase of the surface temperature the steady-state film-wetted area decreases, and eventually maintains constant after the temperature is greater than 190°C. Besides, the temperature also affects the splashing angle (see Figure 8). A stable splashing angle marked by red line is established at higher surface temperature greater than 192°C. The later study of Qiu et al. [71] showed that the inclination of the droplet train decreases the splashing angle and increases the averaged secondary droplet size.
\nThe impact dynamics of droplet train at different surface temperature and the droplet velocity is 15.2 m/s [
Soriano et al. [72] presented an experimental observation of multiple droplet train impingement. Impact spacing between multiple droplet streams would affect spreading and splashing in impact regimes, and the optimal cooling performance was achieved when the film velocity was not disturbed by adjacent droplet streams. Zhang et al. [73, 74] further demonstrated that both impact spacing and impingement pattern significantly affect local and global cooling performance on the hot surface. In comparison with the circular jet impingement cooling, the droplet train impingement achieves a better cooling performance for various impingement patterns. The same conclusion was made when comparing the cooling performance of droplet train and jet impingement on flowing film that cools the hot surface [75]. Through piezoelectric nozzles more groups of jet flow were generated and broke up to droplet train for cooling the hot surface [76], and the maximum heat flux reaches~ 170 W/cm2 with the nozzle diameter of 25 μm. However, unclear impact dynamics and its relation to local cooling need the further study.
\nOur recent studies try to understand spray cooling from droplet burst aspect [75, 77]. Different from droplet train cooling, it assumed that in spray cooling droplet groups impact the surface at a constant frequency rather than droplet train. Each droplet group is defined as a droplet burst, and each burst contains a constant number of droplets, which is called burst size. The frequency at which droplet bursts are generated is called the burst frequency. The generation mechanism of droplet burst was first proposed by Gao and Li [75, 77] and implemented in tests. A droplet generator combined with controlled interrupter is applied for droplet burst generation. A droplet train is ejected from droplet generator with droplet frequency \n
Droplet burst flows are generated by interrupting a droplet train flow (
For the impact of one droplet burst (see Figure 10), at \n
(a) Impact dynamics of a drop burst flow affecting the film flow; (b1) surface temperature distribution at
For the impact of one droplet burst flow, the temperature at impact point is measured. Temperature measurement shows that the burst flow causes the temperature to quickly decrease, and then the temperature fluctuates with the constant fluctuation frequency and amplitude in full-developed stage. The fluctuation frequency is equal to the burst impact frequency. The temperature at the impact point remains lower than the film cooling temperature without droplet burst impact. Heat transfer coefficient shows three development stages of the convection: affecting, restoring, and restored. During the restored stage, local cooling has returned to the film cooling. The restored stage may not exist if the time interval between bursts \n
The comparison of burst flows shows that the trough value of the fluctuating temperature, \n
Spray cooling is one effective cooling technology for handling high-power density and high heat flux removal requirement. In spray cooling, liquid coolant is emitted from a pressurized nozzle and breaks up into numerous secondary droplets affecting heated surface that is covered by radially flowing film. The cooling is achieved through the convection heat transfer from the heated surface to the film flow, nucleate boiling, liquid conduction inside the film flow, and interfacial evaporation from the liquid film. Based on research outcomes reported in the literature, spray cooling technology is reviewed from two aspects: the spray level and the droplet level. In the spray level, these studies emphasize the cooling performance to spray property. Some key properties are summarized in this chapter, involving spray characterization, nozzle positioning, phase change, and enhanced surface. In the droplet level, the studies focus on local heat transfer associated with droplet impact conditions, which are classified into a few categories: impact of single droplet on dry surface, stationary film, flowing film, impact of droplet train, and impact of droplet burst. Although spray impact cannot be simply considered as the superposition of single droplets, the studies in droplet level provide experimental and theoretical basis to explain what happened on heated surface and the relevant local heat transfer mechanism in spray cooling.
\nIntechOpen implements a robust policy to minimize and deal with instances of fraud or misconduct. As part of our general commitment to transparency and openness, and in order to maintain high scientific standards, we have a well-defined editorial policy regarding Retractions and Corrections.
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\\n\\n1.2. REMOVALS AND CANCELLATIONS
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\\n\\nA Statement of Concern detailing alleged misconduct will be issued by the Academic Editor or publisher following a 3rd party report of scientific misconduct when:
\\n\\nIntechOpen believes that the number of occasions on which a Statement of Concern is issued will be very few in number. In all cases when such a decision has been taken by the Academic Editor the decision will be reviewed by another editor to whom the author can make representations.
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\\n\\nA Correction will be issued by the Academic Editor when:
\\n\\n3.1. ERRATUM
\\n\\nAn Erratum will be issued by the Academic Editor when it is determined that a mistake in a Chapter originates from the production process handled by the publisher.
\\n\\nA published Erratum will adhere to the Retraction Notice publishing guidelines outlined above.
\\n\\n3.2. CORRIGENDUM
\\n\\nA Corrigendum will be issued by the Academic Editor when it is determined that a mistake in a Chapter is a result of an Author’s miscalculation or oversight. A published Corrigendum will adhere to the Retraction Notice publishing guidelines outlined above.
\\n\\n4. FINAL REMARKS
\\n\\nIntechOpen wishes to emphasize that the final decision on whether a Retraction, Statement of Concern, or a Correction will be issued rests with the Academic Editor. The publisher is obliged to act upon any reports of scientific misconduct in its publications and to make a reasonable effort to facilitate any subsequent investigation of such claims.
\\n\\nIn the case of Retraction or removal of the Work, the publisher will be under no obligation to refund the APC.
\\n\\nThe general principles set out above apply to Retractions and Corrections issued in all IntechOpen publications.
\\n\\nAny suggestions or comments on this Policy are welcome and may be sent to permissions@intechopen.com.
\\n\\nPolicy last updated: 2017-09-11
\\n"}]'},components:[{type:"htmlEditorComponent",content:'IntechOpen’s Retraction and Correction Policy has been developed in accordance with the Committee on Publication Ethics (COPE) publication guidelines relating to scientific misconduct and research ethics:
\n\n1. RETRACTIONS
\n\nA Retraction of a Chapter will be issued by the Academic Editor, either following an Author’s request to do so or when there is a 3rd party report of scientific misconduct. Upon receipt of a report by a 3rd party, the Academic Editor will investigate any allegations of scientific misconduct, working in cooperation with the Author(s) and their institution(s).
\n\nA formal Retraction will be issued when there is clear and conclusive evidence of any of the following:
\n\nPublishing of a Retraction Notice will adhere to the following guidelines:
\n\n1.2. REMOVALS AND CANCELLATIONS
\n\n2. STATEMENTS OF CONCERN
\n\nA Statement of Concern detailing alleged misconduct will be issued by the Academic Editor or publisher following a 3rd party report of scientific misconduct when:
\n\nIntechOpen believes that the number of occasions on which a Statement of Concern is issued will be very few in number. In all cases when such a decision has been taken by the Academic Editor the decision will be reviewed by another editor to whom the author can make representations.
\n\n3. CORRECTIONS
\n\nA Correction will be issued by the Academic Editor when:
\n\n3.1. ERRATUM
\n\nAn Erratum will be issued by the Academic Editor when it is determined that a mistake in a Chapter originates from the production process handled by the publisher.
\n\nA published Erratum will adhere to the Retraction Notice publishing guidelines outlined above.
\n\n3.2. CORRIGENDUM
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\n\n4. FINAL REMARKS
\n\nIntechOpen wishes to emphasize that the final decision on whether a Retraction, Statement of Concern, or a Correction will be issued rests with the Academic Editor. The publisher is obliged to act upon any reports of scientific misconduct in its publications and to make a reasonable effort to facilitate any subsequent investigation of such claims.
\n\nIn the case of Retraction or removal of the Work, the publisher will be under no obligation to refund the APC.
\n\nThe general principles set out above apply to Retractions and Corrections issued in all IntechOpen publications.
\n\nAny suggestions or comments on this Policy are welcome and may be sent to permissions@intechopen.com.
\n\nPolicy last updated: 2017-09-11
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