PWM-based Class-D audio amplifiers often use analog feedback loops to increase linearity and PSR.
These analog control loops have to satisfy several (contradictory) specifications: high gain in the audio band, a unity-gain bandwidth much smaller than the PWM frequency, large attenuation of harmonics of the PWM frequency...
Generally, the control loops are designed using linear control theory. In that sense, the PWM modulator is often modeled to behave like a linear gain in the frequency of interest. This linear gain is a function of the supply voltage, in relation to the used triangle oscillator amplitude.
My question is: How to build such a Class-D amplifier, which should operate a t different supply voltages? In that case, one component of the linear control loop might change its gain (e.g. by a factor of 3 or more). Such a change in the feedback loop might cause instabilities (Phase Margin), or uncontrolled high frequency switching (PWM Ripple Aliasing) of the amplifier.
Until now, I found 3 possible solutions:
1) Use a triangle oscillator, where the amplitude is a fixed ratio of the supply voltage. Then, the gain of the modulator would not change. However, additional circuit overhead is needed in many cases, to keep the frequency stable.
2) Use a fixed amplitude oscillator, and design the loop gain, such that it tolerates large parameter changes. Yet, this will lead to an inferior control loop.
3) Adapt the loop filter according to the supply voltage, which might be difficult to implement.
Do you have any other suggestions? Which is the best way to go, in your opinion?
Thanks, br
Timucin Karaca
dear Timucin,
before answering this question, I believe it should be pointed out that in the expression of the loop gain of a class D amplifier, the power supply voltage V_DD does not appear only in the expression of the PWM modulator gain (D=v_in / V_DD, where D is the duty cylce and v_in is the input voltage of the PWM modulator), but also in the relation between the (averaged) output voltage and the duty cycle of the square wave, i.e. v_out,ave= D * V_DD for a half bridge, vout= (1-2D)*V_DD for a full bridge, bipolar modulation). In the evaluation of the linearized transfer function from the input of the PWM modulator to the averaged output voltage of the bridge, the V_DD terms cancel and the value of the supply votlage does not have a net impact on the loop gain. Obviously, the situation is different if the bridge and the PWM modulator are intended to operate from different supplies which are not scaled together. Is this your case?
Yes exactly, that is the case. I should have added that in my question. The supply voltage of my bridge is larger than the supply of the PWM modulator. The bridge supply is variable, while the modulator supply is preferably fixed.
Now my question is, if I should try to implement the modulator (=triangle oscillator + comperator) to scale with the variable bridge supply (idea 1), such that VDD cancels out again. OR if I should find a different approach.
It would be interesting to hear some solutions of amplifiers in the field....
If you are using two different supplies, I believe there is also another problem to be addressed: if the closed-loop voltage gain of the amplifier is constant and it is fixed to map the swing of the input signal to the maximum output swing of the class-D amplifier (from 0 to VDD) for the minimum VDD, using the same voltage gain at a higher VDD implies that the full swing is not fully exploited. Maybe you can address both the loop gain problem and the output swing problem by acting of the feedback network. This is easily done using switches if only a discrete set of supply voltages is considered.
When the supply voltage is reduced by a factor alpha, the feedback factor R1/(R1+R2) can be increased by the same factor alpha, so that the loop gain remains the same and the closed loop-gain (1+R2/R1) is reduced by alpha: by so doing, assuming that the output was spanning the full swing, reducing the supply by the factor alpha, the output does not exceed maximum swing. On the other hand, if the supply voltage of the bridge is increased by a factor alpha, the feedback factor is reduced by a factor alpha for the same reason.
What I am implicitly assumed so far is that a fully analog solution is required. If the control loop is implemented digitally, the actual value of the supply can be first acquired and used in the control algorithm.
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