Application of error reduction techniques#
In the previous sections, we have studied basic amplifier biasing techniques. We found means to define the voltage levels and provide bias currents, and we evaluated errors resulting from device tolerances and imperfections. If the biasing errors are too large, we have to apply so-called error reduction techniques to reduce them. This section is devoted to the application of such techniques. We will study them at a conceptual level only.
One error reduction technique that is often applied during biasing is compensation. As a matter of fact, adding level shifts and bias current sources to the design is a form of additive compensation. It has already been discussed in the previous sections and is considered as a basic biasing technique.
If remaining errors are too large, we need more powerful error reduction techniques to reduce them. In section Negative feedback and auto-zero biasing, we will introduce negative-feedback biasing. We have already applied negative feedback for the design of amplifier concepts. In situations in which errors due to biasing can be distinguished from signal excursions, negative feedback biasing may offer further improvement.
Negative feedback and auto-zero biasing#
Similar to the design of negative feedback amplifier configurations, the
conceptual design of negative feedback biasing starts with measurement of the
bias quantity to be fixed. In the amplifier from fig-micAmpADCsystem this is the DC operating voltage at the input of the
ADC. In order to obtain maximum and equal positive and negative digital signal
excursions at its output, the DC input voltage of the ADC should be set to \(2\)V. During our study of biasing errors in section
Evaluation of biasing errors, we found all kinds of error sources that
contribute to an error in this DC voltage. The idea behind negative-feedback
biasing is that we measure this deviation from the desired operating point and
apply a control signal to the amplifier to correct it. However, the output
signal of the amplifier itself also causes such deviations, and those should
not be compensated for! Hence, negative feedback biasing can only be applied
if a distinction can be made between deviations caused by the signal and
deviations caused by operating point changes. Such distinctions can be made in
the frequency domain or in the time domain.
Negative-feedback biasing#
Fig. 311 A. Concept of negative feedback biasing applied to the amplifier from Fig. 301 B. Implementation of the circuit with an integrating transimpedance amplifier as controller.#
Changes in the DC operating point are caused by supply changes, device tolerances, biasing errors and temperature changes. These changes are usually slow and have only frequency components at very low frequencies. If those frequencies do not occur in the signal, a distinction between biasing and signal components can be made in the frequency domain.
Fig. 311 shows a possible concept of negative feedback biasing for the voltage amplifier from Fig. 311A.
The integrating transadmittance amplifier G1 is the bias loop controller. It acts as a first-order low-pass filter with an infinite DC gain. Hence, for DC, it can be replaced with a nullor. As a consequence, the DC output voltage of the amplifier will equal \(V_{ref}\). Since both the input impedance and the output impedance are infinite, the source-to-load transfer, the noise and the power efficiency will not be affected by the bias control loop. This, of course, is under the assumption that the integrator gain \(g_{B}\) has been properly designed. In section High-pass cut-off and DC loop gain, we will study the design of the high-pass cut-off frequency and in Chapter Frequency compensation, we will discuss the design of the high-pass response and see the way in which the stability of negative feedback biasing can be assured. In the following example, we will derive symbolic expressions for the DC output voltage and the voltage transfer from the source to the output.
Example
\label{example-feedbackBiasing}
The netlist of the amplifier from Fig. 311A is shown below:
1VampFeedbackBiasTotal
2* file: VampFeedbackBiasTotal.cir
3* SLiCAP netlist file
4V1 1 0 V value = {V_s}
5V2 6 0 V value = 0 dc={V_ref}
6R1 1 2 {R_s}
7R2 4 5 r value={R} dcvar={(R*sigma_r)^2}
8R3 out 4 r value={19*R} dcvar={(19*R*sigma_r)^2}
9C1 2 3 {C_a}
10C2 5 0 {C_b}
11X1 3 4 out 0 O_dcvar ; amplifier controller
12+ sib={I_b*sigma_Ib}
13+ sio={i_off}
14+ svo={v_off}
15+ iib={I_b}
16G1 3 0 out 6 {g_B/s} ; bias loop controller
17.end
Below, the SLICAP script for evaluation of the DC output voltage, the source-to-load transfer and the high-frequency approximation of the source-to-load transfer.
Fig. 312 SLiCAP analysis results.#
1#!/usr/bin/env python3
2# -*- coding: utf-8 -*-
3# File VampFeedbackBiasTotal.py
4
5from SLiCAP import *
6
7fileName = 'VampFeedbackBiasTotal'
8i1 = instruction() # Creates instance of instruction object
9i1.setCircuit(fileName + '.cir') # Checks, defines the local circuit object,
10 # and sets the index page to the circuit
11 # index page
12i1.setSimType('symbolic')
13i1.setGainType('vi')
14i1.setDataType('dc')
15i1.setSource('V1')
16i1.setDetector('V_out')
17result = i1.execute()
18
19htmlPage('Feedback biasing')
20text2html('The DC output voltage $V_{outDC}$ is:')
21eqn2html('V_outDC', result.dc)
22
23# Laplace transfer function with feedback biasing
24
25i1.setGainType('gain')
26i1.setDataType('laplace')
27result = i1.execute()
28text2html('The voltage transfer $A_v$ from source to load is:')
29eqn2html('A_v', normalizeRational(result.laplace))
30hf = sp.limit(result.laplace, ini.Laplace, 'oo')
31text2html('For high frequencies this can be written as:')
32eqn2html('A_v', hf)
The html page with the results is shown in Fig. 312.
The results comply with our expectations:
The DC output voltage equals that of the reference voltage source.
The transfer has three poles and three zeros.
The high-frequency transfer equals the ideal gain of \(20\).
Fig. 311B shows a possible implementation of this concept. The transadmittance gain \(g_{B}\) is defined by the gain of the transimpedance integrator and the values of R4 and R5:
Auto-zero biasing#
If, during a short time interval, the load signal is not of interest, this time interval may be used to correct biasing errors with a feedback control signal. The corrected biasing should be maintained during the time of interest of the signal, which requires a memory element. If the load signal is not allowed to change due to this auto-zero process, a second memory element is required for storing the signal and passing it to the load during the auto-zero time interval. This principle is applied in so-called auto-zero operational amplifiers.
Modulation and demodulation techniques#
Compensation, negative feedback and auto-zero techniques do not affect the way in which the information is embedded in the signal: they adapt the circuit to the signal. Another approach for reducing the amount of signal processing errors is to do the opposite: adapt the signal to the circuit. As a matter of fact, digitization can be seen as such a technique. By reducing the number of signal levels to two, the signal is made insensitive to nonlinearities that occur in the circuit. Modulation and demodulation techniques also belong to this class of error reduction techniques. With these techniques, the frequency range of a signal can be changed, and this may be an interesting option for the reduction of biasing errors. If frequency components of the signal are in the same range as those of temperature variations, changes in the quiescent operating point of an amplifier due to temperature variations cannot be distinguished from signal excursions. Bringing the frequency range of the signal outside the frequency range of temperature changes and of other possible disturbances will then increase the signal-to-noise ratio. After the modulated signal has been amplified to a level at which temperature variations can be neglected, it can be demodulated to its original frequency band. This principle is applied in so-called chopper-stabilized amplifiers.