Analog to Digital Converters Electronics Unit – Lecture 7 Representing a continuously varying physical quantity by a sequence of discrete numerical values. Prepared by Jim Giammanco <giamman@rouge.phys.lsu.edu> 03 07 10 14 09 02 00 04 LSU 10/28/2004 Electronics 7

Conversion Methods (selected types, there are others) Ladder Comparison Successive Approximation Slope Integration Flash Comparison LSU 10/28/2004 Electronics 7

Ladder Comparison LSU 10/28/2004 Electronics 7 The counter, through a digital-to-analog converter, produces a stairstep of increasing voltage. At each step the input signal is compared to the current step level. If the input is higher, then continue to step, if the imput is equal or lesser, then stop and read the counter. The count value is then read as the numeric value of the input. Note that the conversion will happen faster for low level inputs and will take longest if the input is near the upper end of the range. LSU 10/28/2004 Electronics 7

Single slope integration Charge a capacitor at constant current Count clock ticks Stop when the capacitor voltage matches the input Cannot achieve high resolution Capacitor and/or comparator Vin Counting time Functions much like ladder comparison, except without the need for the digital-to-analog converter. Therefore is simpler to implement, but with a penalty in accuracy, linearity, and repeatability. Start Conversion Start Conversion S Q Enable - + R N-bit Output C Counter IN Oscillator Clk LSU 10/28/2004 Electronics 7

Successive Approximation Starting with the most significant bit, the input is tested against the output of the digital-to-analog converter, and a “HI or LO” decision is made. In general, the conversion time will be independent of the input level, since all bits have to be tested each time. LSU 10/28/2004 Electronics 7

Flash Comparison If N is the number of bits in the output word…. Then 2N comparators will be required. With modern microelectronics this is quite possible, but will be expensive. Fastest of all since all 2N comparisons take place at once. But think of having to implement 256 comparators for an 8 bit conversion – much more expensive. LSU 10/28/2004 Electronics 7

Slope Integration & Ladder Approximation Cheap but Slow Pro and Cons Slope Integration & Ladder Approximation Cheap but Slow LSU 10/28/2004 Electronics 7

Pro and Cons Flash Comparison Fast but Expensive Slope Integration & Ladder Approximation Cheap but Slow LSU 10/28/2004 Electronics 7

Pro and Cons Successive Approximation The Happy Medium ?? Slope Integration & Ladder Approximation Cheap but Slow Flash Comparison Fast but Expensive Most microcontrollers that incorporate A/D conversion use the successive approximation method since the necessary computer resource is already present. LSU 10/28/2004 Electronics 7

Resolution Suppose a binary number with N bits is to represent an analog value ranging from 0 to A There are 2N possible numbers Resolution = A / 2N LSU 10/28/2004 Electronics 7

Resolution Example Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with an 8-bit A/D converter 2.5 / 28 = 0.0098 V, or about 10 mV per step 300 K / 28 = 1.2 K per step LSU 10/28/2004 Electronics 7

Resolution Example Temperature range of 0 K to 300 K to be linearly converted to a voltage signal of 0 to 2.5 V, then digitized with a 10-bit A/D converter 2.5 / 210 = 0.00244V, or about 2.4 mV per step 300 K / 210 = 0.29 K per step Is the noise present in the system well below 2.4 mV ? LSU 10/28/2004 Electronics 7

Quantization Noise e.g. 8 bit → 49.8 db, 10 bit → 61.8 db Each conversion has an average uncertainty of one-half of the step size ½(A / 2N) This quantization error places an upper limit on the signal to noise ratio that can be realized. Maximum (ideal) SNR ≈ 6 N + 1.8 decibels (N = # bits) e.g. 8 bit → 49.8 db, 10 bit → 61.8 db Compare the digitization SNR to the SNR of the analog input. It’s foolish to use a 62 db A/D to read a signal has a SNR of just 30 db. LSU 10/28/2004 Electronics 7

Signal to Noise Ratio Recovering a signal masked by noise Some audio examples In each successive example the noise power is reduced by a factor of two (3 db reduction), thus increasing the signal to noise ratio by 3 db each time. In the first example the signal and noise power are approximately equivalent, so the SNR is about 0 db. This means the ratio of (signal plus noise) to (noise) will be about 3 db. This level is generally accepted as the “minimum discernable signal” (MDS) in radio practice. Example 1 Example 2 Example 3 Example 4 LSU 10/28/2004 Electronics 7

Conversion Time Time required to acquire a sample of the analog signal and determine the numerical representation. Sets the upper limit on the sampling frequency. For the A/D on the BalloonSat board, TC ≈ 32 μs, So the sampling rate cannot exceed about 30,000 samples per second (neglecting program overhead) While BalloonSat can sample quite fast, there is limited memory for data storage. 1000 samples per second would fill memory in less than a minute. LSU 10/28/2004 Electronics 7

Data Collection – Sampling Rate The Nyquist Rate A signal must be sampled at a rate at least twice that of the highest frequency component that must be reproduced. Example – Hi-Fi sound (20-20,000 Hz) is generally sampled at about 44 kHz. External temperature during flight need only be sampled every few seconds at most. LSU 10/28/2004 Electronics 7

Human Successive Approximation Converter Activity E7a Do the HuSAC ® a party game for techies... Human Successive Approximation Converter LSU 10/28/2004 Electronics 7

Data Acquisition Using BalloonSat Activity E7b Data Acquisition Using BalloonSat LSU 10/28/2004 Electronics 7