AD-DA_Converters.doc 9/19/2008 12:18 PM Page 1 Voltage Measurement Digital To Analog Converters Most A/D and D/A converters utilize operational amplifiers. The figure below shows a typical D/A converter using a resistance network. The switches are electronic, controlled by the bits in a digital word:AD-DA_Converters.doc 9/19/2008 12:18 PM Page 2 The total current flowing from the resistor network is: 2,3(7.10 )MMmm refm m - 1m=1 m=10cI = = , = cIE1 R2 Since no current can flow into the op-amp, this must equal the feedback current, and 1 2,3 (6.65 , 7.11 )orM -1mref rmm=0ref rM -1 M -2 M -30 1 2 M -1M -1 = I ERc= ERR2 ER= [ + + +.... + ]c c c c2 2 2R 2 The total number of bits will determine the minimum step in the analog output. A 12 bit D/A converter will have a resolution of 1 part in 4096 of full scale. (212 = 4096)AD-DA_Converters.doc 9/19/2008 12:18 PM Page 3 Analog to Digital Converters Most analog to digital converters work by means of successive approximation. The analog voltage is compared successively with test voltages generated by a D/A converter:AD-DA_Converters.doc 9/19/2008 12:18 PM Page 4 Successive approximation of "45" with a 6 bit ADC. Most of today’s mixed-signal programmable system chips (PSCs) include a configurable successive approximation register (SAR) analog-to-digital converter (ADC). These ADCs are often the architecture of choice for: medium-to-high resolution applications with sample rates under 5 megasamples per second (Msps) and resolution ranging from 8 to 16 bits.AD-DA_Converters.doc 9/19/2008 12:18 PM Page 5 This resolution is sufficient for a variety of applications, such as portable or battery-powered instruments, industrial controls and data or signal acquisition. Ramp ADC are typically slow but highly accurate. A known ramping voltage is compared with the input. The time is takes the ramping voltage to reach the input voltage is proportional to the input voltage. Parallel or flash ADC are very fast but low resolution. Typically reserved for dedicated or stand-alone instruments.AD-DA_Converters.doc 9/19/2008 12:18 PM Page 6AD-DA_Converters.doc 9/19/2008 12:18 PM Page 7 Sigma-Delta ADC high resolution low cost slow to modest speedAD-DA_Converters.doc 9/19/2008 12:18 PM Page 8 They are a good ADC choice for applications such as process control and weighing scales. The analog side of a sigma-delta converter (a 1-bit ADC) is very simple. The digital side, which is what makes the sigma-delta ADC inexpensive to produce, is more complex. It performs filtering and decimation. Oversampling and decimation: if a signal is sampled many times and averaged the resulting error is reduced.AD-DA_Converters.doc 9/19/2008 12:18 PM Page 9 Typical Application of Sigma-Delta ADCs Thermocouple Measurement with Cold-Junction Compensation 3-Wire and 4-Wire RTD Configurations Other low level, low frequency signalsAD-DA_Converters.doc 9/19/2008 12:18 PM Page 10 Because the conversion requires a finite time, a sample and hold amplifier is used to maintain a constant input voltage during the conversion.AD-DA_Converters.doc 9/19/2008 12:18 PM Page 11 Analog to Digital Conversion Errors Quantization Error: The resolution is limited by the finite number of bits. A 12 bit A/D converter has a resolution of 1 part in 4096 full scale. This is the minimum change in the input voltage which can be detected. A/D Resolution is defined as: Q = EFSR/2M where EFSR is the Full Scale Range of the A/D. The FSR may vary in data acquisition systems with variable input signal gain. EFSR = EMax FSR/Gain Our systems, National Instruments 6025E, have a maximum FSR or +/- 10 Volts, a maximum gain of 200 and a resolution of 12 bits. QMin = 20/1/212 = 20/4096 = 4.88 milliVolts QMax = 20/200/212 = 0.10/4096 = 24.4 microVolts The available gains are 1, 2, 20 and 200 resulting in EFSR = ±10, ±5, ±0.5 and ±0.05 Volts. The resolution, Q, therefore ranges from about 5 mV to 24 VAD-DA_Converters.doc 9/19/2008 12:18 PM Page 12 Signal-to-Noise Ratio: (SNR) relates the power of the signal, given by Ohm’s Law as E2/R, to the power that can be resolved by quantization, given by E2/R2M. The SNR is the ratio of these two values. Defined in terms of the decibel this gives: SNR [dB] = 20 log 2M Saturation Error: If the analog voltage is outside the range of voltage which the A/D converter can generate, the D/A amplifier will saturate. A digital signal will still result but it will no longer approximate the analog signal. This is usually evident by looking at the output. -8.0E+00-6.0E+00-4.0E+00-2.0E+000.0E+002.0E+004.0E+006.0E+008.0E+000.000 0.200 0.400 0.600 0.800 1.000Time (seconds)Amplitude (volts)Simulated Data Simulated Sine InputAD-DA_Converters.doc 9/19/2008 12:18 PM Page 13 Conversion Error: This includes all of the analog errors that occur, including electrical noise, temperature effects, droop in the sample and hold amplifier,