The components connected between the INJ pin and inject capacitor establish a damped injection network. Damping is specifically required to manage resonance between the CM choke inductance and inject capacitance, which manifests in the AEF loop gain as a pair of complex zeros.

Figure 9-3 highlights three specific RC branches: R_D1, R_D1A and C_D1 form one branch from the INJ pin; R_D2 and C_D2 in series connect to GND; R_D3 and C_D3 in parallel connect to the inject capacitor.

Based on the injection mechanism, the AEF circuit presents a low shunt impedance to CM noise. Given the three damping impedance branches highlighted in Figure 9-3, Equation 1 approximates the AEF impedance as:

where the term G_AEF is the gain from the power lines to the INJ node (see the TPSF12C1 quickstart calculator for related detail).

Equation 1 shows that the impedance Z_INJ appears in series with Z_D3 and a parallel combination of Z_D1 and Z_D2. Furthermore, the gain G_AEF is reduced by the voltage divider ratio between Z_D2 and Z_D1. These effects combine to increase the effective impedance of the AEF and hence reduce its attenuation performance, thus illustrating a trade-off between performance and stability.

So while an injection network is needed for stability, it also adds impedance in series with the inject capacitor, thus compromising EMI mitigation. As shown below, the user can minimize the impact on performance with careful and appropriate design.

Illustrated in Figure 9-4, at low frequencies in the range of 5 kHz to 50 kHz, components R_D1 and C_D2 provide compensation and R_D3 damps the effects of LC resonance. At higher frequencies (above 10 kHz), the dominant component impedance of each branch transitions to enable better attenuation performance:

• R_D1 transitions to C_D1
• C_D2 transitions to R_D2
• R_D3 transitions to C_D3

Finally, C_D1 transitions to R_D1A if needed for phase margin of the AEF loop at high frequencies, typically above 100 kHz. When viewed in a clockwise direction, Figure 9-4 shows these transitions in sequence as frequency increases.

Below are basic guidelines to select the component values for the injection network:

1. The undamped loop gain characteristic is likely to be unstable within the range of 5 kHz to 50 kHz, which, as mentioned previously, relates to an LC resonance between CM choke inductance and inject capacitance. Observe from circuit simulation – or by using the TPSF12C1 quickstart calculator – the frequency, f_LFstability, at which the phase crosses –180° with positive gain, indicating negative gain margin.
2. Choose a corner frequency with R_D1 and C_D2 equal to one fifth of the instability frequency:
   Equation 2.
   Assigning R_D1 = 1 kΩ and assuming instablity at 35 kHz, use Equation 3 to find a value for the capacitance of C_D2:
   Equation 3.
3. Select C_D1 < C_D2, where a typical choice is C_D1 = C_D2/5 = 4.7 nF.
4. Choose the resistance of R_D2 such that the R_D2, C_D2 corner frequency is equal to that of R_D1, C_D1:
   Equation 4.
5. Select the resistance of R_D3 to damp the resonance around the instability frequency, f_LFstability.
   • A typical choice for R_D3 is 500 Ω to 1 kΩ.
   • Assign C_D3 equal to C_INJ or a suitable value such that the R_D3, C_D3 corner frequency is less than switching frequency.
   • A lower resistance for R_D3 results in more damping but at the penalty of reduced high-frequency attenuation (or forces a higher value for C_D3 to maintain the applicable corner frequency below the switching frequency).
6. Select a resistance for R_D1A of 50 Ω to improve the phase margin of the AEF loop (if needed).