CMOS Analog IC Design Page


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1 CMOS Analog IC Design Page NYQUIST FREQUENCY ANALOGDIGITAL CONVERTERS The sampled nature of the ADC places a practical limit on the bandwidth of the input signal. If the sampling frequency is f S, and f B is the bandwidth of the input signal, then f B < 0.5f S which is simply the Nyquist relationship which states that to avoid aliasing, the sampling frequency must be greater than twice the highest signal frequency.
2 CMOS Analog IC Design Page CLASSIFICATION OF ANALOGDIGITAL CONVERTERS Analogdigital converters can be classified by the relationship of f B and 0.5f S and by their conversion rate. Nyquist ADCs  ADCs that have f B as close to 0.5f S as possible. Oversampling ADCs  ADCs that have f B much less than 0.5f S. Table Classification of AnalogtoDigital Converter Architectures Conversion Rate Nyquist ADCs Oversampled ADCs Slow Integrating (Serial) Very high resolution >14 bits Medium Fast Successive Approximation 1bit Pipeline Algorithmic Flash Multiplebit Pipeline Folding and interpolating Moderate resolution >10 bits Low resolution > 6 bits
3 CMOS Analog IC Design Page STATIC CHARACTERIZATION OF ANALOGTODIGITAL CONVERTERS DIGITAL OUTPUT CODES Table Digital Output Codes used for ADCs Decimal Binary Thermometer Gray Two s Complement
4 CMOS Analog IC Design Page INPUTOUTPUT CHARACTERISTICS Ideal inputoutput characteristics of a 3bit ADC
5 CMOS Analog IC Design Page DEFINITIONS The dynamic range, signaltonoise ratio (SNR), and the effective number of bits (ENOB) of the ADC are the same as for the DAC Resolution of the ADC is the smallest analog change that can be distinguished by an ADC. Quantization Noise is the ±0.5LSB uncertainty between the infinite resolution characteristic and the actual characteristic. Offset Error is the horizontal difference between the ideal finite resolution characteristic and actual finite resolution characteristic Gain Error is the horizontal difference between the ideal finite resolution characteristic and actual finite resolution characteristic which is proportional to the analog input voltage.
6 CMOS Analog IC Design Page INTEGRAL AND DIFFERENTIAL NONLINEARITY The integral and differential nonlinearity of the ADC are referenced to the vertical (digital) axis of the transfer characteristic. Integral Nonlinearity (INL) is the maximum difference between the actual finite resolution characteristic and the ideal finite resolution characteristic measured vertically (% or LSB) Differential Nonlinearity (DNL) is a measure of the separation between adjacent levels measured at each vertical step (% or LSB). DNL = (D cx  1) LSBs where D cx is the size of the actual vertical step in LSBs. Note that INL and DNL of an analogdigital converter will be in terms of integers in contrast to the INL and DNL of the digitalanalog converter. As the resolution of the ADC increases, this restriction becomes insignificant.
7 CMOS Analog IC Design Page EXAMPLE OF INL and DNL
8 CMOS Analog IC Design Page MONOTONICITY A monotonic ADC has all vertical jumps positive. Note that monotonicity can only be detected by DNL. Example of a nonmonotonic ADC: If a vertical jump is 2LSB or greater, missing output codes may result. If a vertical jump is 1LSB or less, the ADC is not monotonic.
9 CMOS Analog IC Design Page EXAMPLE INL and DNL of a 3bit ADC Find the INL and DNL for the 3bit ADC shown on the previous slide. Solution With respect to the digital axis: 1.) The largest value of INL for this 3bit ADC occurs between 3/16 to 5/16 or 7/16 to 9/16 and is 1LSB. 2.) The smallest value of INL occurs between 11/16 to 12/16 and is 2LSB. 3.) The largest value of DNL occurs at 3/16 or 6/8 and is +1LSB. 4.) The smallest value of DNL occurs at 9/16 and is 2LSB which is where the converter becomes nonmonotonic.
10 CMOS Analog IC Design Page DYNAMIC CHARACTERISTICS The dynamic characteristics of ADCs are influenced by: Comparators Samplehold circuits Circuit parasitics Logic propagation delay
11 CMOS Analog IC Design Page COMPARATOR The comparator is the quantizing unit of ADCs. Openloop model: Nonideal aspects: Input offset voltage, V OS (a static characteristic) Propagation time delay  Bandwidth (linear) A v (s) = A v (0) s + 1 ω c  Slew rate (nonlinear) T = C V I = A v (0) sτ c + 1 (I is constant)
12 CMOS Analog IC Design Page LINEAR PROPAGATION TIME DELAY (Small input changes) If V OH and V OL are the maximum and minimum output voltages of the comparator, then minimum input to the comparator (resolution) is v in (min) = V OH  V OL A v (0) If the propagation time delay, t p, is the time required to go from V OH or from V OL to V OH +V OL, then if 2 v in (min) is applied to the comparator, the t P is, V OH  V OL 2 Therefore, t p is = A v (0) [1 e t p/τ c ] v in (min) = A v (0) [1 e t V p/τ c ] OH  V OL A v (0) t p (max) = τ c ln(2) = 0.693τ c If v in is greater than v in (min), i.e. v in = kv in (min), then t p = τ c ln 2k 2k 1 Illustration of these results:
13 CMOS Analog IC Design Page NONLINEAR PROPAGATION TIME DELAY (Large input changes) The output rises or falls with a constant rate as determined by the slew rate, SR. t p = T = V SR = V OH  V OL 2 SR (If the rate of the output voltage of the comparator never exceeds SR, then the propagation time delay is determined by the previous expression.)
14 CMOS Analog IC Design Page EXAMPLE Propagation Delay Time of a Comparator Find the propagation delay time of an open loop comparator that has a dominant pole at 10 3 radians/sec, a dc gain of 10 4, a slew rate of 1V/µs, and a binary output voltage swing of 1V. Assume the applied input voltage is 10mV. Solution The input resolution for this comparator is 1V/10 4 or 0.1mV. Therefore, the 10mV input is 100 times larger than v in (min) giving a k of 100. Using the previous expression for this case, we get t p = ln = 103 ln = 5.01µs If the output is slewrate limited, then t p = 1 2 1x10 6 = 0.5µs Therefore, the propagation delay time for this case is the larger or 5.01µs. Note that the maximum slope of the linear response is Max dv out dt = d dt A v (0)[1e t/τ c](0.01v) = A v (0) e τ t/τ c(0.01v) = A v (0) = A v (0)ω c = = 0.1V/µs c 100τ c Since the maximum rate of the linear response is less than the slew rate, the response is linear and the propagation time delay is 5.01µs.
15 CMOS Analog IC Design Page APERATURE JITTER IN S/H CIRCUITS Illustration: If we assume that v in (t) = V p sinωt, then the maximum slope is equal to ωv p. Therefore, the value of V is given as V = dv in dt t = ωv p t. The rms value of this noise is given as V(rms) = dv in dt t = ωv p t 2 2. The aperature jitter can lead to a limitation in the desired dynamic range of an ADC. For example, if the aperature jitter of the clock is 100ps, and the input signal is a full scale peaktopeak sinusoid at 1MHz, the rms value of noise due to this aperature jitter is 111µV(rms) if the value of V REF = 1V.
16 CMOS Analog IC Design Page INPUTOUTPUT TEST FOR AN ADC Test Setup: TESTING OF ADCs The ideal value of Q n should be within ±0.5LSB Can measure: Offset error = constant shift above or below the 0 LSB line Gain error = contant increase or decrease of the sawtooth plot as V in is increased INL and DNL (see following page)
17 CMOS Analog IC Design Page ILLUSTRATION OF THE INPUTOUTPUT TEST FOR A 4BIT ADC
18 CMOS Analog IC Design Page MEASUREMENT OF NONLINEARITY USING A PURE SINUSOID This test applies a pure sinusoid to the input of the ADC. Any nonlinearity will appear as harmonics of the sinusoid. Nonlinear errors will occur when the dynamic range (DR) is less than 6N db where N = number of bits. Comments: Input sinusoid must have less distortion that the required dynamic range DAC must have more accuracy than the ADC
19 CMOS Analog IC Design Page FFT TEST FOR AN ADC Test setup: Comments: Stores the digital output codes of the ADC in a RAM buffer After the measurement, a postprocessor uses the FFT to analyze the quantization noise and distortion components Need to use a window to eliminate measurement errors (Raised Cosine or 4term BlackmannHarris are often used) Requires a spectrally pure sinusoid
20 CMOS Analog IC Design Page HISTOGRAM TEST FOR AN ADC The number of occurances of each digital output code is plotted as a function of the digital output code. Illustration: Comments: Emphasizes the time spent at a given level and can show DNL and missing codes DNL where DNL(i) = Width of the bin as a fraction of full scale Ratio of the bin width to the ideal bin width 1 = H(i)/N t 1 P(i) H(i) = number of counts in the ith bin N t = total number of samples P(i) = ratio of the bin width to the ideal bin width INL is found from the cumulative bin widths
21 CMOS Analog IC Design Page COMPARISON OF THE TESTS FOR ANALOGDIGITAL CONVERTERS Other Tests Sinewave curve fitting (good for ENOB) Beat frequency test (good for a qualitative measure of dynamic performance) Comparison Test Error DNL Missing Codes INL Aperature Uncertainty Noise Bandwidth Errors Gain Errors Offset Errors Histogram or Code Test Yes (spikes) FFT Test Sinewave Curve Fit Test Yes Beat Frequency Test Yes Yes (Elevated noise floor) Yes (Bin counts with zero Yes (Elevated noise Yes Yes counts) floor) Yes (Triangle input gives Yes (Harmonics in Yes Yes INL directly) the baseband) No Yes (Elevated noise Yes No floor) No Yes (Elevated noise Yes No floor) No No No Yes (Measures analog bandwidth) Yes (Peaks in distribution) No No No Yes (Offset of distribution average) No No No
22 CMOS Analog IC Design Page BIBLIOGRAPHY ON ADC TESTING 1.) D. H. Sheingold, AnalogDigital Conversion Handbook, Analog Devices, Inc., Norwood, MA 02062, ) S.A. Tretter, Introduction to DiscreteTime Signal Processing, John Wiley & Sons, New York, ) J. Doernberg, H.S. Lee, and D.A. Hodges, FullSpeed Testing of A/D Converters, IEEE J. of SolidState Circuits, Vol. SC19, No. 6, December 1984, pp ) Dynamic performance testing of A to D converters, Hewlett Packard Product Note 5180A2.
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