In this part, we go to greater depths to look at TL431 dynamics. Adjust your air regulator for the deeper dive. What is seen in the data sheet plots of gain and output resistance for some manufacturers is at first hard to believe.

**Frequency Response**

The Texas Instruments plot of frequency response is reproduced below from the TI *Power Supply Circuits* databook of 1996, page 3-29.

The static open-loop voltage gain magnitude with *R*_{L} = 232 Ω||(15 kΩ + 8.25 kΩ) ≈ 230 Ω is about 52 dBV or about 400. It decreases by 3 dBV at about 10 kHz and has a unity-gain frequency, *f*_{T}, of around 3 MHz. Linear projection places it under 2 MHz, at about 1.8 MHz. The slope of the linear part of the curve is not –1, or –20 dBV/decade, but is –30 dBV over two decades. A line drawn from an endpoint at (1 MHz, 0 dB) to (10 kHz, 50 dB) is parallel with the plot and has a slope of –1.5. Ordinarily, circuit slopes have integer values. The noninteger value indicates that a combination of poles and zeros is interacting to determine the slope.

To compare with another manufacturer, the ON Semiconductor TL431 plot is copied below (from Motorola *Analog/Interface ICs Device Data*, 4Q95, DL128D REV 5, page 5-22). It too has a slope of about –30 dBV over two decades (or –1.5) but its dominant pole is at about 12 to 15 kHz. It too has a zero at about 700 kHz. The test circuit is identical to that of TI and is comparable to the TI plot.

To confirm the slope, a line with –1.5 slope is fitted to the ON gain plot below.

Now compare these plots to the corresponding plot in the PDF data from the NXP (Philips) website below. (The Linfinity TL431 plots are similar.) The quasistatic gain is about the same but the pole frequency is at about 5 kHz. The plot gives a hint of a doublet (pole-zero pair) near 1 MHz. The *f*_{T} is about that of the TI part and is about 3 MHz. The log-log plot shows a slope in the linear region of close to –1, as it should be for single-pole roll-off. The quasistatic gain for the given *f*_{T} is thus about 600 or 55.6 dBV.

The Intusoft and ON Semi SPICE library models agree somewhat with the TI and ON data. The model from the Intusoft Library is essentially the same as the ON Semiconductor model, given below.

The SPICE netlist is drawn as a circuit diagram below.

The G2 transconductance has a value of 1.73 S = 1/0.578 Ω, and G1 has a value of 0.11 S = 1/9.091 Ω. The TL431 quasistatic *G*_{m} is calculated as

Then multiplying this transconductance value by the above gain-test-circuit *R*_{LG} = 230 Ω, it is about 683 or 56.7 dBV, about 4.7 dB higher than the 400 of the TI plot and closer to the 500 of the ON plot. With a gain closer to the lower value of 400, *G*_{m0} is closer to the G2 model value and is 1/0.575 Ω. The model gain appears high.

The R1, C1 pole of the SPICE model is at about 20.4 kHz. The pole and zero of the R2, C2, R3 network are at *p* = 18.1 kHz and *z* = 199 kHz. This results in a frequency response plot of voltage gain with a two-pole (–2 slope) roll-off at about 20 kHz, breaking to a –1 slope at about 200 kHz. This is closer to the TI and ON plots than the NXP plot.

The TL431 amplifier does not have a single-pole response because of noninteger slopes of the TI and ON log-log plots. A Mathcad plot of two poles at 20 kHz and a zero at 200 kHz is shown below, with line segments labeled with their slopes. At a decade higher in frequency, the zero modifies the slope of the two poles. A line with a slope of –2 fitted to the curve between poles and zero is clearly too steep. The fit of a line with slope of –1.5 explains the slope of the TL431 plots. Above the zero frequency, the plot becomes asymptotic to a slope of –1.

In the sixth and final part of this TL431 series, we finish with dynamic response involving the output impedance.