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.

**Output Impedance**

The plots shown below are that of the output impedance as given by TI (Figure 1) and ON (Motorola) (Figure 2).

**Figure 1**

**Output impedance**

**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 *Z _{o} * 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, *Z _{o} * is that of the closed-loop circuit and is

where *G* is the voltage gain of the forward-path amplifier and *H _{V} * 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 *Z _{o} * ,

The first factor is the closed-loop *Z _{o} * , reduced by the quasistatic (0

^{+}Hz) feedback factor, 1 +

*G*x

_{0}*H*. The zero at

_{V}*p*causes it to increase until it flattens at the pole frequency at (1 +

*G*x

_{0}*H*) x

_{V}*p*. For

*Z*=

_{o}*r*,

_{out}By writing *Z _{o} * (cl) in continued-fraction form using long division, an equivalent circuit impedance results:

Interpreting the final expression, *r _{out} * is in parallel with a series LR where

*L*is

*r*/

_{out}*p*x

*G*x

_{0}*H*and

_{V}*R*is

*r*/

_{out}*G*x

_{0}*H*. For high loop gain,

_{V}*r*/

_{out}*G*x

_{0}*H*can be omitted and

_{V}*Z*(cl) approximated as a high-frequency model, valid for frequencies between

_{o}*p*and

*G*x

_{0}*H*x

_{V}*p*, as

,

Above amplifier bandwidth, *p* – somewhere between 70 kHz and 100 kHz on the ||*Z* || plots – the impedance increases as loop gain decreases, in accordance with the above equation. Then when loop gain reaches one – at about 1.2 MHz to 1.6 MHz – the plot breaks again at the value of the open-loop *r _{out} * .

The 10 Ω to 12 Ω values of *r _{out} * as read from the above impedance plots are lower than

*r*||

_{o}*R*= 123 Ω ||1 kΩ = 110 Ω. The National Semiconductor

_{L}*Z*semi-log plot is similar but peaks around 1.1 MHz and 14 Ω before decreasing to about 12.5 Ω. According to the above

_{o}*Z*model, the

*Z*plot should break at a pole frequency of about 400 x 85 kHz or 34 MHz, not 1.4 MHz. If

*Z*were to continue to rise to 34 MHz,

*r*would be around 400 x (0.2 Ω) = 80 Ω, closer to the calculated 110 Ω. If the above plots were extended to 34 MHz, then

_{out}*r*would be about (34/1.4)·(11 Ω) = 267 Ω, higher than the calculated value.

_{out}The NXP log-log plot of *Z _{o} * is shown below. While it also has a zero around 70 kHz, unlike the previous two plots, it shows no break frequency around 1 MHz. Its slope is close to +1, in accordance with a single zero.

The plot also shows the intimation of another break frequency at 2 MHz, where *Z* ≈ 5.5 Ω. The inductance is thus

This inductance can resonate with output capacitance in the high-frequency region, where there is a capacitance range that can cause oscillation.

**Closure**

The noninteger slopes of the TI and ON gain and impedance plots, the intimation of a zero break in the gain plots of TI and ON near the unity-gain frequency, the flattening of *Z _{o} * after 1.2 decades of 1.5 slope, and the upturn in

*Z*of the ON plot at about 3.7 MHz contribute to the invalidation of a single-pole model for the TI and ON TL431. The NXP and Linfinity TL431 data fit the single-pole theory.

_{o}The TL431 is typical of analog circuits. On the surface, they seem simple enough, but when diving into them, it is found that their depth can give some engineers the bends. I hope some of what has been presented in this dual three-part article about the TL431 has cleared the waters somewhat and will make future diving into this part less troublesome.

Thank you for sharing this useful series of articles.