We return for a second wind and to the surface for air as we catch our breath in Part 4 by considering two categories of application circuits for the TL431.
The TL431 can be used either as a voltage feedback amplifier stage with local feedback or as an open-loop transconductance amplifier such as the error amplifier within a larger power-converter feedback loop as shown below. The input, νi , is the incremental output voltage of the converter. The R1, R2 voltage divider is the feedback path and the error amplifier is the first stage of the forward path.
The corresponding total-variable block diagram is shown below. From the circuit diagram,
To is the current divider fraction of pin-3 current that becomes i0. The total error is
Then for incremental analysis, this reduces to
The incremental transfer function of the circuit is thus
HV and Gm are both positive quantities so that when νi increases, io increases. Then the incremental output current contributed by the TL431 is
The voltage transfer function of the TL431 path is
The TL431 Gm amplifier output current develops an output voltage across rout. To is the fraction of TL431 output current that flows through the optocoupler diode. For an ideal current-source output, rout → ∞ so that To = 1.
Another use of the TL431 is as an inverting op-amp voltage amplifier with external RL. In this use, R2 does not affect the op-amp closed-loop gain because it forms an input divider, Ti and is included also in H, which is 1 – Ti. In the closed-loop feedback equation, the interaction of the Ti and H factors eliminate R2 in the closed-loop gain equation. However, if there is no static feedback - no resistor from output to op-amp inverting input - then the op-amp is open-loop at 0+ Hz and the circuit reverts at 0+ Hz to the previous circuit, where R2 was part of an input divider to the amplifier. The TL431 has sufficient gain that when it is in a larger feedback loop, its gain is typically excessive, causing instability.
To reduce the inverting op-amp gain while allowing the R1, R2 divider to set the output voltage of the converter, capacitively-coupled feedback can be used. The simplest is a single feedback capacitor, Cf from TL431 output to input. Then the input divider is thevenized, with series resistance Ri= R1||R2 and the divided source. The voltage gain is
The loop gain is significantly reduced by the pole if it is low enough in frequency, and it might also contribute to the compensation of the converter output storage capacitor zero caused by series resistance.
Finally, do not forget the passive forward path, 1/Rf. Its current (not voltage) has the same polarity as (is in phase with) the active path through the TL431. Depending on the value of ro, it can be of some significance when the active-path rout (cl) increases at increasing frequencies. For large ro, it is not significant.
In the next part, we plunge deeper as we begin to look at TL431 dynamics.