High-Efficiency Analog Amplifiers, Part 1: The Efficiency-Linearity Tradeoff

Switching amplifiers, like switching power supplies, are more efficient than linear or analog amplifiers. However, the analog amplifier is not obsolete just yet; new circuit ideas improve its efficiency to be comparable to switching amplifiers. This article presents some of those ideas.

Because of their extreme nonlinearity (of having only two output levels), digital amplifiers (usually called “Class D” – remember D for digital ) are inherently inferior to analog amplifiers (“Class A” – A for analog – or “Class AB”, analog, barely ) in fidelity, or what might be called audio precision . Yet audio is going the way of digital amplifiers because of their higher efficiency with a generally acceptable amount of distortion. Analog power amplifiers, such as those for audio, are seemingly doomed to extinction. However, new circuit ideas can improve their efficiency, resulting in the best of both high efficiency and linearity. With monolithic integration, some analog amplifiers might also be lower in cost than digital amplifiers, though this is a system-level consideration.

The challenge is to design an amplifier with bipolar output that can deliver some significant power. Historically, the first advancement toward greater efficiency was the so-called “Class B” amplifier, shown below.

Ideally, such an amplifier has zero crossover distortion. That is, around 0 V out, there is no deadband where neither transistor is conducting, as is the case in the above circuit, with a deadband of about +/-VBE . Deadband causes distortion, though the above amplifier is more power efficient than the worst case “Class A” amplifier without deadband, shown below.

The average output power of this amplifier, by Watt’s Law, is

To show this as a warm-up exercise for efficiency derivations, suppose the output waveform is a sine-wave,

Then at any phase angle of the sine-wave, the instantaneous power dissipation of the output is

If the average is found by integrating this over a cycle of sine-wave, the average output power is

The amplifier output power is maximum whenever the sine-wave is at the top of its curve (sin θ = 1), and vO = Vo = Vg , the supply voltage;

At Vo = Vg , there is no voltage across the transistor and no power dissipation in it. No power is dissipated in the amplifier circuit at this point in the sine-cycle and efficiency is maximum.

The negative half-cycle is symmetrical in that (–Vg )2 = Vg 2 in the above equation, and they are equal. In the negative case, vO = –Vg and there is no voltage across RL , no current in it, and no power dissipation.

The power dissipation in the transistor, again invoking Watt’s Law, is

When the sine-wave covers the maximum amplifier range, Vo = Vg , average transistor and supply powers are

The power dissipated in the transistor must be

To maximize efficiency ,

power dissipation in Q is minimized. At what fraction of P o (max) is it minimized?

To solve this problem, let output power be expressed as a fraction of its maximum;

Then P Q for P o (n ) is

To find at which value of n that P Q is minimum, take the derivative and set to zero;

Solving for n , the minimum P Q occurs whenever

Therefore, P Q is minimum whenever the output sine-wave has an amplitude of

We saw previously that maximum η occurs for Vo = Vg , but for minimum power loss in Q, it is the sine average value of Vg .

A Class AB amplifier is between Class A and B in that the output transistors are biased so that there is no deadband and that they are both always conducting. This is the typical case for analog audio amplifiers, and some of the finesse in the design is to make the biasing stable over time and temperature.

Historically, it became a fad to designate different amplifier topologies by a “Class X ” designation, where X is a letter than means nothing in itself. After so many of these letters, they become annoying to try to remember, and I do not generally use them. (Class D is where I quit.)

We will find that an important aspect of the quest for efficient analog amplifiers is the power supply itself. One way to achieve high efficiency is to use supplies with voltages that track the output waveform. Tracking supplies make the amplifier efficient but they also turn the supplies into amplifiers. The problem has merely been moved to the supplies. With switching supplies, it is possible without much additional expense to provide constant voltage outputs at multiple voltages. This is the key to efficient analog amplifiers and figures in to the schemes in the following Parts of this article.

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