Class D amplifiers

Archive
Class D amplifiers
Links
About this site
History

Forum
Home

What is Class D?

Power amplifiers are often categorized in different classes. See the Usenet Audio FAQ, if you don't know what class A, class B and class AB is.

Class D refers to a design where the (unfiltered) output of a amplifier circuit is always at one of two extreme voltage levels ("low" or "high"). This means that the conducting elements at the output of the amplifier are switched between the on-state and the off-state. Thus, an element at the output deliveres current into the load when the voltage over the same element is (close to) zero, and it does not deliver any current when the voltage is high over the same element.

Such an output with only two output levels can of course not deliver a continous voltage of a varying amplitude (e.g. a music signal) into a load directly. Instead, the output is made to switch between the two output levels at a very high frequency - substantially higher than the highest audible frequency. This is done by feeding a high-frequency square-wave signal to the power amplification stage, where the pulse-width ratio is varied in order to make the avereged (filtered) output signal follow the (amplified) input signal very closely.

Pulse-width modulation

There are different ways of creating a pulse-width modulated signal. A common one is to compare an analog input signal with a high-frequency triangle wave, and drive the output to high when the input is higher than the momentary triangle wave voltage, and drive the output to low otherwise. This creates a pulse-width modulated output signal, with a switch frequency equal to the frequency of the triangle wave.
(This is however not the principle employed in the Sorensen Audio Experiment design; see the archives for details.)

The picture below is included for illustrative purposes only. It is the output of a test setup (on a breadboard) of the Sorensen Audio Experiment version 3.0. The horisontal time scale is one microsecond/div, and the horisontal scale is 20V/div. So, this is a pulsewave of just over 1MHz, with about 100V peak-to-peak.

Some properties of class D

The output transistors are switched between saturated and cut-off state. This gives a high efficiency, since there is a low voltage drop over the transistor while it is delivering current into the load. So, you can use smaller and cheaper output transistors at a given effective output power.
And since the efficiency is higher, compared to class A or B, the power supply can also be made smaller/cheaper.
The output stage is like a 1-bit D/A converter, which is by definition perfectly linear. (In a N-bit Digital-to-analog converter, the linearity is measured in terms of how closely the 2N possible output voltage values align on a straight line when plotted against the digital input value. When there are only two points on the line, they automatically align perfectly :-)
So, the power output stage is perfectly linear, avoiding the cross-over distortion found in class AB designs. Instead, the class D output stage introduces a quite severe distortion to its amplified signal. This is countered for by using feedback, and noise shaping (see below).
The high-frequency switching introduces a challenge in terms of PCB (printed circuit board) design, to avoid EMI (Electro-Magnetic Interference) emission. Also, the output of the amplifier needs to be filtered, in order to stop the high-frequency components on the output to propagate out on the speaker cables.

Theoretical analysis of class D operation

(To fully appreciate the analysis below, the reader is assumed to be familiar with mathematical transform techniques, like the Laplace-transform.)

Generally, it is well-known that using feedback around an amplifier, it is possible to trade off raw amplification ability against different other properties. Such as bandwidth, high input impedance, or reduction of distortion.

Think of a one-bit analog-to-digital quantizer, for example realized as a simple comparator. It is self-evident that the result will be very poor if you try to sample a signal with it - it can only detect the zero-crossings in the input signal, and nothing else. 

But in some sense, the one-bit quantizer is something that does let an input signal through, although severly distorted. This is something that can be exploited, using feedback.

Place this distorting element in a feedback loop. Also, introduce a loop filter according to the figure below. The quantizer is modeled as a source of distortion, or noise. That is, a noise signal Q(s) is added to the output of the loop filter.
(X(s) and Y(s) denote the Laplace-transform av the corresponding continous variables x(t) and y(t) respectively. H(s) is the transfer function of the loop filter, and ß is the feedback factor (usually < 1))

The output signal Y(s) can be expressed as:

Y(s) = Q(s) + H(s) (X(s) - ßY(s))

If this is solved for Y(s), then

Y(s) =

 H(s) X(s) +  1 Q(s)
1+ßH(s) 1+ßH(s)

Now you can see the benefit of the feedback loop. Suppose to begin with that H(s)=a, where a is a (high) constant amplification factor > 106. Then the first term in the expression above can be simplified to X(s) / ß, and the second term can be simplified to Q(s) / aß. This shows that the desired signal X(s) is amplified by a factor 1/ß, while the undesired quantization noise is amplified by 1/aß, which in effect is a powerful suppression of the noise if a is large.

If you instead use an integrator as the loop filter (i.e. a low-pass filter with H(s)=a/s), then the second term in the expression for Y(s) above will take on a high-pass characteristic. The total noise power (summed over all frequencies) is thereby actually increased, but it can be shown that the noise power is decreased in the lower part of the frequency spectrum. This is what is referred to as noise shaping.

(The deeper theory behind noise shaping is not elaborated here, please refer to the article on Principles of Oversampling A/D Conversion, by Max W. Hauser. It is referenced on the links page.

 

Do you have feedback or questions regarding the Audio Experiment Project, or this web - please E-mail Johan Sorensen.
For anything that may be of general interest, why not use the forum...
Last updated: januari 27, 2002.