An audio power amplifier is built from stable stages

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Feedback, operational amplifiers and analogue signal processing · Signals, systems, control and digital signal processing

Inside the Instrument, Ch Stability and compensation

Problem

An audio power amplifier is built from stable stages, so its open loop has no right-half-plane poles, and its loop gain

T(j\omega)

has been measured across the band. Its unity-gain crossover is at

f = 100\,\text{kHz}

, where the phase is

-140^\circ

. Lower down, the phase falls through

-180^\circ

2\,\text{kHz}

, where

|T| = 3.0

, reaches about

-195^\circ

near

5\,\text{kHz}

, and climbs back through

-180^\circ

12\,\text{kHz}

, where

|T| = 1.6

. At every other frequency the phase stays above

-180^\circ

. Someone argues: "The loop crosses

0\,\text{dB}

only once, at

100\,\text{kHz}

, where the phase margin is

180^\circ - 140^\circ = 40^\circ

. A positive margin at the only

0\,\text{dB}

crossing means the amplifier is unconditionally stable, whatever the operating point." Under heavy clipping the amplifier's gain block loses

6.0\,\text{dB}

of gain at every frequency, shifting

|T(j\omega)|

down by that amount everywhere without changing its phase. ((a)) Find the error in the reasoning. ((b)) Find where

T(j\omega)

crosses the negative real axis once the amplifier is clipping, and decide whether it stays stable.

Browse the problem library