2 AEF compensation

Figure 2-1(a) shows an AEF with no compensation. In Figure 2-1, V_S is a noise source, Z_S is the internal impedance, Z_L represents the impedance of line-impedance stability networks or power sources, C_in represents the input capacitors of power converters, L is the differential-mode inductor, C_sense and C_inj are the sensing and injection capacitors, R_{DC_fb} is to provide DC feedback for the Op_amp and C_para is the parasitic capacitance between the power trace and ground.

As an op amp-based feedback circuit, the AEF in Figure 2-1(a) could become unstable, which would saturate the op amp. In such cases, the performance of the AEF could be significantly affected, and the AEF may consume more power and inject extra noise into the system [3]. Since the loading network of the op amp is complex, the AEF in Figure 1a could be unstable at both low and high frequencies.

At low frequencies (such as between 10 kHz and 50 kHz), the phase of the loop gain can go to positive 180 degrees and the system can become unstable, primarily because of the voltage dividers formed by C_inj and L, and by C_sen and R_{DC_fb}. One method for low-frequency compensation is to add R_comp and C_comp in parallel with R_{DC_fb}, as shown in Figure 2-1(b). C_comp is for low-frequency compensation by making the feedback network capacitive at low frequencies. R_comp is to ensure the performance of the AEF. In addition, there are typically electrolytic capacitors at the input of the converter to store energy and ensure converter stability. The equivalent series resistance (ESR) of the electrolytic capacitors also helps with low-frequency stability.

At high frequencies, the output impedance of the op amp and C_para will generate a pole and cause phase lag of the loop gain. In addition, op amps typically have a low-frequency pole. As a result, the loop gain will have two poles at high frequency and its phase goes close to negative 180°, which can cause high-frequency instability. R_comp1 and C_comp1 in Figure 2-1(b) are for high-frequency compensation, which can be 100 nF and 0.5 Ω. R_comp1 and C_comp1 can boost the phase of the loop gain at high frequencies so that the system has enough phase margin to ensure high-frequency stability. In certain applications, high-frequency ceramic capacitors (such as 10 nF or 100 nF) are necessary for high-frequency noise filtering or for protection circuits, such as smart diodes for reverse protection. In such cases, there are several ways to maintain high-frequency stability:

• Insert ferrite beads between the sense/inject node and the high-frequency ceramic capacitors to decouple them.
• Add small resistors in series with the high-frequency capacitors for compensation.
• Place high-frequency capacitors far from the AEF, since the ESRs and equivalent series inductances (ESLs) of the ceramic capacitors and printed circuit board traces can also help with high-frequency stability.

Overall, it is essential to make sure that the impedance of the sense/inject node to ground is not dominated by capacitance at high frequencies (between 10 MHz to 50 MHz).