## Saturday, February 6, 2021

### Audio Amplifier Feedback - NCore style compensation

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

After analyzing the two-pole compensation scheme with the C-R-C "T" network, it became clear that compensating an audio amplifier is not just about ensuring stability, but about shaping (usually maximizing) the loop gain in the audio range of frequencies. This can be achieved in many different ways, and here is another one.

At the 131st AES convention in 2011, Bruno Putzeys presented a paper titled High-Order Analog Control of a Clocked Class-D Audio Amplifier with Global Feedback Using Z-Domain Methods, discussing the details of then-new Class D amplifier technology, marketed by Hypex under the trade name NCore. An NCore amplifier has an analog control loop with five poles, one real plus two complex pairs. One pair comes from the LC output filter, and the others come from the following circuit:

An opamp is enclosed in a local feedback loop, part of which is the same C-R-C "T" network that is used in the two-pole compensation scheme. $R_f$ and $C_f$ add another pole-zero pair, and the transfer function of the whole circuit has the following form:
$$H(s)={v_o(s) \over v_i(s)}={A \over s}{(s+\omega_{z1})(s+\omega_{z2}) \over {s^2+{\omega_0 \over Q}s+\omega_0^2}}$$where $\omega_{z1}={1 \over {R_f C_f}}$, $\omega_{z2}={1 \over {R_t (C_1 + C_2)}}$, and $\omega_0=\sqrt{1 \over {R_f R_t C_1 C_2}}$.
That is, it includes an integrator (pole at $\omega=0$), zero at $\omega_{z1}$, a pair of poles with the corner frequency $\omega_0$, and another zero at $\omega_{z2}$, in this order. The positions of all poles and zeros can be chosen freely, although some values may be impractical given the parasitics.

For example, with the first zero at 72Hz, the pair of poles at 46kHz, and the second zero at 720kHz, the Bode plot looks like this:

Light blue is the Bode plot of an amplifier with NCore compensation network around its second stage. The gain set by the global feedback is the blue trace. As in previous posts, for comparison are also shown the same amplifier uncompensated (green) and with two-pole compensation (red).

This compensation network keeps the loop gain at about 55dB in the audio range of frequencies. (As I posted earlier, some experts believe that a flat loop gain across the audio range has a more palatable sonic signature compared to that of the loop gain falling at higher frequencies.) As the frequency increases beyond the corner frequency of the pole pair, the loop gain falls, first at 40dB/decade, then at 20dB/decade, ensuring sufficient phase margin and thus stability.