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Design Article

Understanding output filters for Class-D amplifiers

1/9/2008 2:28 PM EST

Common-Mode Filters
Common-Mode Filters
Common-mode filters are L-C filters with one side of the capacitor grounded. The inductor is placed in series with the amplifier output(s) and the capacitor is connected from the speaker terminal to ground. Since single-ended amplifier filters already have one side of the capacitor grounded the low-pass filter is a common-mode filter.

When used with an amplifier with BTL outputs, the filter shown in figure 1 would be a differential filter since it filters the signal between the two outputs. Common-mode filters for amplifiers with BTL outputs are different than the differential low-pass filter. The filter inductance for BTL amplifier outputs is normally split into two separate inductors, with one inductor is placed in series with each of the amplifier outputs. Each inductor has half of the total inductance required for the low-pass filter.

Because the capacitance across the load is now the series combination of the two capacitors for BTL outputs, each capacitor needs to be twice the value calculated for the low-pass filter so that the total capacitance will be correct. Note that because the inductance for each BTL output is cut in half but the capacitance to ground is twice the normal value, the resonant frequency of the common-mode filter is the same as the resonant frequency of the differential filter.

fC = 1/(2π√(LTCT)) = 1/(2π√(½LT • 2CT))

The simplest common-mode L-C filter is just an inductor and a capacitor to ground (figure 3). This produces excellent attenuation at high frequencies but this filter has an underdamped common-mode response that can cause unwanted ringing on the speaker leads. It can also cause very high ripple current through the inductor and capacitor. The impedances of the inductor and capacitor cancel at the resonant frequency so the current at the resonant frequency is only limited by the stray resistance in the circuit (primarily the output impedance of the amplifier and the DC resistance of the inductor).

Figure 3: A simple common-mode filter and its response

In order to damp the common-mode response of the filter it is necessary to add some resistance to the filter. Normally a resistor is added between the capacitor and ground.

However, adding a resistor between the capacitor and ground creates a zero in the filter response which can greatly reduce the filter's effectiveness at higher frequencies. The effects of adding a resistor in series with the capacitor can be seen in the following plot. Note that the amplitude of the resonant peak is greatly reduced but the attenuation at high frequencies is also reduced.

Figure 4: Common-mode filter response with damping resistors in series with the capacitors

For this reason a second capacitor is usually placed across the resistor to create a pole above the filter's resonant frequency. This pole cancels the effect of the zero created by the resistor at higher frequencies while allowing the resistor to provide damping at the L-C resonant frequency. Figure 5 shows the response of a filter with a capacitor in parallel with the damping resistor. Note that the resonant peak of the filter is still much lower than without a damping resistor but the attenuation at high frequencies is much better than without the second capacitor.

Figure 5: Common-mode filter response with bypass capacitors in parallel with the damping resistors.

Calculating the component values for a common-mode filter is easy. The total inductance and capacitance in the filter remains the same as for a differential-mode filter:

LT = RL/(2πfC) and CT = 1/((2πfC)2 • (LT))

Because the inductance for BTL outputs is divided between two inductors in series, however, the value of each inductor is equal to ½ of the total inductance

L1 = L2 = ½LT = RL/(4πfC)

Similarly, the capacitance for each filter is divided between two capacitors in series, so the value of each capacitor is equal to twice the total capacitance

C1 = C2 = C3 = C4 = 2/((2πfC)2LT) = 1/((2πfC)2L1)

The value of the common mode resistors should be

R1 = R2 = 1/(√2 • 2πfCC1)

This resistor value will insure that the zero is below the L-C resonant frequency and the pole is above the LC resonant frequency, allowing the resistor to damp the filter response at the resonant frequency.

Using a common-mode filter has another beneficial effect. The response of a differential-mode filter is normally damped by load (the speaker). However, if the amplifier is operated without a speaker connected the response of the filter will be very underdamped, similar to the response shown in figure 3. The use of a common-mode filter with damping resistors will ensure that the filter response is always well behaved, even without a speaker attached.

entuitive

12/6/2008 11:30 PM EST

well stated, the elegance of simplicity-takes me back to the day working with audio engineers.