Thin out your breathing mixture as we take the final plunge into TL431 dynamics and consider the output impedance. More strange creatures are sighted at this depth, yet all ends in a good dive.
The plots shown below are that of the output impedance as given by TI (Figure 1) and ON (Motorola) (Figure 2).
Dynamic Impedance vs. frequency
The log-log plots have the same basic shape and a non-integer slope of about 1.5. The TI plot changes two decades in Zo over a ×20 frequency range (ratio) to result in a slope of 1.54. The pole frequency for TI is at about 1.2 MHz and zero at 70 kHz, a ratio of 17. For ON, the pole is at about 600 kHz and zero at 50 kHz, a ratio of 12.
The basic plot shape is characteristic of feedback amplifiers. Below the loop-gain bandwidth, Zo is that of the closed-loop circuit and is
where G is the voltage gain of the forward-path amplifier and HV is the voltage attenuation of the divider feedback path from the output to pin 1. For a single-pole G of bandwidth, p,
It is substituted into the closed-loop expression for Zo,
The first factor is the closed-loop Zo, reduced by the quasistatic (0+ Hz) feedback factor, 1 + G0 x HV. The zero at p causes it to increase until it flattens at the pole frequency at (1 + G0 x HV) x p. For Zo = rout,
By writing Zo (cl) in continued-fraction form using long division, an equivalent circuit impedance results: