8.2.2.10.2 Voltage Loop Compensation

We choose a standard configuration for a TL431 / optocoupler based feedback network. Type 2 loop compensation is appropriate for a design using peak current mode control. First we set the DC operating points for the TL431 (U1) and the optocoupler (U2).

We assume that the optocoupler (U2) has a current transfer ratio (CTR) of 1 and choose to operate it at a maximum LED current, I_F of 10 mA. R_D is then given by:

Equation 103.

We set the parallel combination of R_G and R_F to 2.4 kΩ for a nominal 10-dB gain for output perturbations via the direct path from R_D to the optocoupler diode. This path exists in parallel with the path through R_A and the TL431. The direct path is important at frequencies where the gain of the TL431 integrator has fallen to 0 dB.

R_G and R_F form a potential divider whose function is to keep the EAP pin within the upper limit of its common mode input range (V_{CM_MAX} = 3.6 V) when there is no current in the photo-transistor. R_G is connected to VREF and this constraint on the voltage at the EAP pin gives:

Equation 104.

Since we know the parallel value of R_F and R_G and their ratio (R_F/R_G), we calculate RF as follows:

Equation 105.

and

Equation 106.

At low frequencies the gain is dominated by the response of the TL431 error amplifier which is configured as a pure integrator. The TL431 has a typical open loop gain of about 60 dB at DC, which decreases at the normal –20 dB per decade. Its gain will be 0 dB when the impedance of CE falls to that of RA. Even though the TL431 gain has fallen to 0 dB, the system still has 10-dB gain due to the direct path through RD.

We put the zero due to capacitor C_E and resistor R_A at the desired 0-dB gain frequency of 2 kHz. Since R_A is already selected from V_OUT setpoint considerations we calculate C_E as follows:

Equation 107.

The optocoupler has a 10-dB response through the direct path, to perturbations on V_OUT. At higher frequencies the capacitance at the collector of the optocoupler (C_F) forms a pole with the resistor in series with the optocoupler LED. The gain then rolls off in half a decade to reach 0 dB. With CF = 68 nF this pole is at about 2.8 kHz.

Having chosen the component values in the feedback path around the TL431 we can draw a Bode Plot of the VOUT to EAP transfer function G_C(f).

The control to output transfer function of the power train is approximated by:

Equation 108.

where

• s = 2πjf is the complex frequency
• s_PP is F_SW / 2 = 50 kHz in this case
• The overall loop response is then given by G_C(f). G_C(o).

This loop response has a crossover frequency of 7.5 kHz. TI recommends that you check the loop stability of the final design with load transient tests and by checking that the gain and phase margins are sufficient. R_LOOP provides a convenient point to inject signals for loop gain and phase measurements. The feedback network may need to be adjusted to achieve satisfactory performance.