Feature: Electronic design


differential pair, minimising DC offset at the amplifier’s output. It is necessary to eliminate second-order distortion generated by the input stage, but the mirror also doubles the transadmittance of the stage and doubles its symmetrical current sourcing and sinking ability for a given input compared to those obtainable with a resistive load. Degeneration resistors R1 and R2 equalise the currents by swamping variations in the base-emitter voltages of transistors Q1 and Q2. Te second stage, comprising Q6, Q7 and bootstrapped


resistive load R9, is effectively linearised and converted into a near-ideal transimpedance amplifier stage (TIS) by minor loop shunt (voltage) derived, shunt (current) applied (admittance), frequency-dependent negative feedback, courtesy of the Miller compensation (or stabilising) capacitor C2. Forward-path transimpedance gain local to the second stage is a product of its current gain and the effective impedance at its output. Terefore, emitter-follower Q6 increases forward-path gain local to the TIS (and, therefore, minor loop gain through C2) by increasing the second stage’s effective current gain. Moreover, the increase in current gain provided by emitter-


follower Q6 allows the bootstrapped resistive load R9 to be made sufficiently small, to allow enough current through to drive the compensation capacitor without significantly reducing the amplifier’s forward-path gain. Although the bootstrapped resistor R9 that constitutes the TIS’s load is quite small at 75Ω, its effective value is greatly increased by the bootstrapping provided by the approximately-constant base-emitter voltage of emitter-follower Q8 across it; see Figure 2. You will notice, the effective impedance with the compensation capacitor remains constant at roughly 22kΩ from DC to about 1Hz, falling to about 41Ω at 20kHz. Tis fall is also replicated at its input and is due in both cases to the shunt (voltage) derived, shunt (current) applied, negative feedback provided by the compensation capacitor.


TIS Te graph of the TIS’s output impedance against frequency was obtained by first opening the major negative feedback loop at the frequencies of interest. Tis was done by connecting a very large capacitor (1GF) from the inverting input of the differential stage to ground, which maintains 100% DC negative feedback while eliminating negative feedback at the frequencies of interest. An ideal grounded independent current source was then connected to the collector of the TIS – the base of bootstrapping emitter-follower Q8 – and an AC analysis run with respect to the independent current source. Te graph of Figure 2 was thus obtained of the ratio of voltage to current at the output of the independent test current source. Note that an ideal independent current, not an ideal independent voltage source is used to provide the test stimulus, because voltage test source has zero output impedance and would merely short the TIS’s output to ground and thereby upset the circuit’s quiescent conditions. If an ideal independent voltage source is used, it must be AC coupled to the TIS’s output by a large capacitor (1kF). Te two dominant poles in the forward path of the amplifier


44 December 2021/January 2022 www.electronicsworld.co.uk


occur in the TIS, and one great advantage of this topology is the minor loop negative feedback (courtesy of the Miller compensation capacitor C2), which causes its dominant pole to migrate to a lower frequency while the first non-dominant pole migrates to higher frequency; this is sometimes called “pole splitting”. Te TIS is effectively a current-controlled voltage source


(CCVS) at the frequencies of interest and, ideally, requires infinitely large source and load impedances for maximal transimpedance gain. Tese conditions are approached in the circuit of Figure 1 by using a current mirror as the input stage’s load and using the Class A emitter-follower Q8 to both bootstrap the TIS’s resistive load and isolate it from the output stage. Te active-current-source-biased Class A emitter-follower


Q8, whose base-emitter voltage defines the constant quiescent current through R9 also palliates the non-linear loading of a Class B output stage on the TIS, thus reducing the distortion generated by this mechanism. Note, however, that just as the shunt positive feedback applied by resistor R9 to the input of Q8 increases its input impedance – the impedance at the TIS’s output – the shunt- derived positive feedback due to resistor R9 also increases the output impedance of Q8. Tis is the opposite of what happens with shunt-derived, shunt-applied negative feedback – such as the Miller minor negative feedback loop – which reduces both input and output impedances. Tus, the output impedance of Q8 in Figure 1 is increased by the shunt-derived positive feedback due to resistor R9, and is about 1.5kΩ at DC, falling to roughly 370Ω at 20Hz and 8Ω at 20kHz; see Figure 3. Tis decrease in the output impedance of Q8 with increasing


frequency is due to the minor loop negative feedback: the positive feedback applied by resistor R9 works to increase the output impedance of Q8, while the negative feedback applied by compensation capacitor C2 works to subvert it by reducing Q8’s source impedance, which in turn results in a reduction in its output impedance. For this reason, incidentally, there is virtually nothing to be gained by connecting the Miller compensation capacitor C2 directly to the output of emitter-follower Q; the resulting deterioration in the stability margins of the minor negative feedback loop with this connection is not trivial. Notwithstanding the increase in its output impedance


occasioned by the positive feedback, the output impedance across the audio band of Q8 is still small enough to render negligible the voltage across it, while driving the non-linear input impedance of a Class-B output stage, provided the input impedance of the output stage is at least 4kΩ at low audio frequencies and throughout the amplifier’s output voltage swing. Tis is roughly ten times the output impedance of emitter-follower Q8 at 20Hz, where, as previously noted, it has its highest output impedance of approximately 370Ω within the audio band.


Single-stage differential folded cascode voltage amplifier Te circuit of Figure 4 consists of a pair of complementary differential stages driving a pair of complementary common base


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