SAR ADC simulated performance.
Analog to digital (A/D) converters provide the interface between the real world (analog) and the digital processingdomain. The analog signals to be converted may originate from many transducers that convert physical phenomena like temperature, pressure or position to electrical signals. Since these electrical signals are analog voltage or current proportionals to the measured physical phenomena, its necessary to convert them to digital domain to conduct any computational. Nowadays, the development of the IC technology resulted in a growth of digital systems. A/D converters are present in the automotive industry, embedded systems and medicine for example. Thus, A/D converters have become important and the large variety of applications implies different types of A/D conversions.
For the A/D type considerations, the analog input should be characterized as one of the following three basic signal types .
Direct current (DC) or slowly varying analog signals.
Continuous changing and single event alternating current (AC) signals.
For sampling the first type of signals, typical A/D conversion architectures are slope, voltage to frequency, counter ramp and sigma-delta. The second signal type is better sampled using the successive approximation, multistep and full parallel A/D conversion architectures. The last signal type uses successive approximation, multistep, pipeline and full parallel architectures.
After choosing the A/D converter architecture, it is important to keep in mind that any of them have nonlinearities that degrade the converter performance. These nonlinearities are accuracy parameters that can be defined in terms of Differential Nonlinearity (DNL) and Integral Nonlinearity (INL). Both have negative influence in the converter Effective Number of Bits (ENOB) .
Differential Nonlinearity (DNL) is a measure of how uniform the transfer function step sizes are. Each one is compared to the ideal step size and the difference in magnitude is the DNL.
Integral Nonlinearity (INL) is the code midpoints deviation from their ideal locations.
Therefore it is important to design implementations capable of improving the ADCs performance by improving DNL and INL.
Physiological signals have amplitudes ranging from tens of
2. Biomedical Application
Advances in low power circuit designs and CMOS technologies have supported the research and development of biomedical devices that can be implanted in the patient. These devices have a sensor interface specially designed to acquire physiological signals, usually composed of an operational amplifier with programmable gain and reconfigurable band-width features, low pass filter and an A/D converter [8, 10]. The signals are acquired and digitalized in the sensor, thus protecting data from external noise interference.
Specific research on A/D converters for biomedical application is focused on design low power circuits regardless of the monotonic feature, once DNL error is above
3. Conventional SAR architectures
Figure 1 illustrates the block diagram of the conventional SAR architecture. It is composed of a Successive Approximation Register that controls the operation and stores the output converted digital data, of a digital-to-analog converter stage (DAC), a comparator usually built with a operational amplifier and of a sample and hold circuit. The output can be taken serially from the comparator output or parallel from the SAR outputs.
The operation consists on evaluating and determining the bits of the converted digital word, one by one, initiating from the most significant bit. Thus the SAR architecture uses
The internal DAC stage, illustrated in Figure 1 is usually designed using capacitor networks that are susceptible to mismatches caused by the fabrication process variation, since the design is based on absolute capacitance values. These mismatches affect the converter accuracy, thus increasing the DNL and INL errors.
4. Proposed Architecture
The presented architecture aims to eliminate the mismatches introduced during fabrication process by replacing the conventional internal DAC based on capacitor networks by a digital PWM modulator circuit and a first order low pass filter.
Figure 1 shows the block diagram of the proposed architecture (dotted line) as a modification on a conventional one (full line).
A PWM signal can be stated in terms of an even function, as illustrated in Figure 2 . By using Fourier series, it can be represented in terms of equations (1) to (4).
By performing the integral on a PWM signal with amplitude
That result shows that the PWM signal consists of a DC level and a square wave of zero average, as illustrated in Figure 3. Only the DC level is necessary in order to implement an internal DAC stage, since any DC level varying from zero to
A way of recovering the DC level is to low pass filter the PWM signal. Since there is no ideal filter, the recovered DC level will have a certain ripple, as illustrated in Figure 4.
This section provides the modeling of a
A macro level simulation is performed using MatLab in order to validate the architecture. Electrical and post layout simulations are performed using Spectre simulator. The A/D converter Layout is developed in
4.1.1 Successive Approximation Digital Logic
The Successive Approximation logic evaluates every digital word output bit according to the clock (CLK) signal. Thus, initiating by the most significant bit, one by one, the bits are evaluated and determined, until the last significant bit. Figure 4 illustrates the SAR digital circuit. The control logic is based on a simple shift register. There is also a flip-flop array that stores the input selection (SEL) that is attached to the comparator output.
On a reset (RST) signal, the shift register is loaded with 10000 and the flip-flop array is loaded with 0000. The combinational logic based on OR gates assures the value 1000 at the output (
One special feature is to use an extra flip-flop in the shift register to indicate the end of conversion (END), enabling the converted digital word to be read in the rising edge of the fifth clock pulse.
4.1.2 Low Pass Filter
Circuits powered by
4.1.3 Digital PWM Modulator
The digital PWM modulator circuit is capable of varying the duty cycle of the output (PWM) according to the digital input word (
On a reset (RST) pulse, the counter resets to
4.1.4 Inverter Based Comparator
The inverter based comparator circuit is used in order to decrease power consumption, since there is no quiescent power consumption. Figure 8 illustrates the comparator stage that uses a low power consumption architecture .
The circuit uses lagged clock signals to avoid overlapping, therefore assuring that the switches
The previous subsections illustrated the functional models for each stage of the proposed
The comparator must evaluate every time the SAR tests a new bit, so they have to be synchronized by the same clock signal. Assuming that all
Now, the low pass filter time constant ought to be determined. Equation (9) shows the cut off frequency for the first order filter.
From Figure 1, it can be observed that the filter must respond faster or at least at the same rate the SAR tests each bit. Thus, equation (11) states the maximum time constant for the low pass filter.
The frequency of the PWM signal must have to be characterized in order to be properly filtered. Since there is no ideal filter, the filtered signal will present a ripple. The PWM signal can be stated in terms of DC level and a sum of even harmonics, as in 12.
Taking into account only the even harmonics, as stated in 13, the energy carried by them can be determined.
It is known that the energy is proportional to
. The maximum energy occurs at
Equation 14 shows that the cosine term is independent of the duty cycle
It can be observed that
Equation 16 shows that the maximum energy in each harmonic is obtained at different duty cycles.
Since there is no ideal filter, after the low pass filtering, the harmonics will not be completely eliminated, but attenuated. It is necessary to evaluate the minimum attenuation required by system, once it is directly linked to ripple amplitude present in the filtered DC level.
Since the first harmonic caries the most energy, it is reasonable to take just it into account to characterize the low pass filter.
Thus, considering the first harmonic (
It is important to notice that the cosine term introduces a variation interval of
Figure 9 illustrates two sequential quantization levels defined by the filtered PWM signal. If the ripple present in two sequential quantization levels overlaps, the converter will lead to a wrong conversion.
Thus, equation (19) states the minimum attenuation necessary to keep ripple under an acceptable value.
Since equation (19) expresses the attenuation in
Finally, the PWM generator design requires a clock frequency
Figure 11 shows the circuit layout that occupies
It can be observed that the proposed architecture improved the A/D Converter accuracy, since the DNL and INL values are less then 0.1 LSB and also that it consumes low power.
|Supply Voltage||2.5 V|
|Max. Sampling frequency||200 Hz|
|ENOB (@166.67 Hz)||3.7549-b|
|Power Consumption||16 uW|
|FoM (Figure of Merit)||7.11 nJ/conv.-step|
Figure 12 shows the post layout simulation of DNL and INL for a slow ramp input. The values are good, lower than
Figure 13 illustrates the output frequency spectrum for a
6. Future Research
The 4-bit layout was fabricated trough MOSIS education program. The prototypes will be tested and the results will be compared to the simulations.
After chip characterization, a proper integrated low pass filter will be implemented in a new prototyping. A new ADC with a larger number of bits will be developed in order to better investigate the non-linearities, ENOB and FoM results.
In order to validate the proposed architecture, a
They also contributed to improve A/D converter accuracy, since the SNDR was improved to
The feature of being almost fully digital contributes to reduce the circuit complexity, the silicon area and power consumption.
The features of high accuracy and low power consumption make the proposed architecture suitable for biomedical applications.
This architecture can be extended to build higher resolution converters by only adding more hardware to the digital stages or building pipeline structures.
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