## Gain consideration using a shunt regulator and optocoupler feedback

The TI TL431 from Texas Instruments plus optocoupler feedback circuit is a common combination when designing power converters. Heed this advice with examples, 4 equations, and 18 figures.
By John Bottrill April 2, 2012

The Texas Instruments TL431 and optocoupler configuration is common combination for many power converter designers. However, without careful design and forethought, design headaches can result. Avoid the pitfalls that trip many inexperienced, and even some experienced, designers.

[Note: TI TL431 is a three-terminal adjustable shunt regulator, with specified thermal stability over applicable automotive, commercial, and military temperature ranges. The output voltage can be set to any value between Vref (approximately 2.5 V) and 36 V, with two external resistors.]

Figure 1 shows a typical circuit. R1 and R2 set up a voltage divider so that at the desired output voltage the junction voltage of R1 and R2 is equal to the TL431’s internal reference voltage. Resistor R3 and capacitors C1 and C2 provide the needed feedback- loop compensation around the TL431 to stabilize the control loop. These components are calculated and added after the rest of the loop gain is determined.

Figure 1. Typical feedback circuit for the TL431, three-terminal adjustable shunt regulator. Courtesy: Texas Instruments.

The circuit gain in Figure 1 around the TL431 is calculated from

Equation 1: Gain = Zfb/R1.

Where Zfb is (Equation 2)

Equation 2:

And ω is the symbol for radians/sec.

The optocoupler loop gain requires that the designer know the optocoupler’s current transfer ratio (CTR). This gain is equal to (R6/R4)*CTR of the optocoupler (Equation 3).

Equation 3:

Optocoupler = CTRx(R6/R4)

However, in Figure 1 the total gain of the TL431 circuit includes an additional factor because the actual transfer function is based upon the current through the optocoupler’s LED. The function is (VOUT–Vcathode)/R4, where VOUT is equal to the VSENSE voltage into the TL431. This leads to a total gain equation for the TL431 and optocoupler (Equation 4):

Equation 4:

In this article, the +1 term is the hidden feedback path that can be ignored, as long as the Zfb/R1 term is significantly greater than one. This term is explained further in this article and in the following scope pictures. For now, let’s assume that the formula is correct as written.

The designer can get the plot of the power converter’s open-loop gain as a function of frequency without the effect of the feedback circuit by multiplying all the remaining converter’s gain elements together. These elements include transformer turns ratio, the pulse width modulation (PWM) gain output filter component effects, corresponding load effects, all the gain elements except for the gain of the TL431, and the optocoupler’s effects. Once this is plotted, the designer can determine the gain as a function of frequency required from the TL4321 and from the optocoupler to meet the loop’s desired stable crossover.

Margin for component tolerances

The converter operates at a specific-switching frequency. The designer knows that the total open-loop gain must cross zero dB at a point below one-sixth of that frequency. Most designers leave a margin for component tolerances while others simply design to cross over at approximately one-tenth of that value. Normally, this margin will more than compensate for component tolerances. In this example, that is assumed and the switching-frequency is fixed at 100 kHz.

Since the control-to-output gain at the desired crossover-frequency is known, all that is needed is to have the feedback loop around the TL431 and the optocoupler’s gain equal to the reciprocal of that value at the crossover frequency.

The designer now can choose the components for the feedback around the TL431 because the frequency needed is known for the loop to cross zero dB. Also needed is a phase margin greater than 45 degrees.

If the gain required from the TL431 circuit is greater than 20 dB, then by choosing the correct resistors and capacitors for R3, C1, and C2, the gain of the TL431 can be shaped. Therefore, the designer can ignore the +1 term as it is small compared to the gain of the TL431.

Figure 2 shows a control-to-output plot of a converter where the gain at the desired zero crossing of 10 kHz is 0.1 or –20 dB. This plot requires a gain from the feedback loop of +20 dB or a factor of 10 at the desired zero crossing.

Figure 2. Control-to-output gain of converter. Courtesy: Texas Instruments

Now, a designer can determine the desired loop response and select the values of R1, R2, R3, R4, R6, C1, and C2 accordingly.

For ease of design in this example, R4 and R6 are equal to each other, and an optocoupler with a CTR of 100 is selected (or, for every milliamp of current through the LED there is one milliamp of current out of the transistor).

The gain desired should be a factor of 10 at 10 kHz, so R3 is equal to 10 R1. The gain of the TL431 should roll off after the zero dB point, but the designer will also want some phase margin. Therefore, the capacitor C2 is set so that it is equal to R3 at 20 kHz. The designer needs gains at low frequencies to be higher, but the phase at crossover should be greater than 45 degrees, so C1 is set to be equal to R3 at 1 kHz.

Figure 3. The control-to-output, TL431, and total system loop gains are shown as a function of frequency. Courtesy: Texas Instruments

Figure 3 shows the initial open-loop gain of the control-to-output (solid line), the compensation gain (dotted line), and the combined total system gain (dashed line). In this example, the design works well. The total loop crosses zero dB (one on Figure 3) at 10 kHz with a slope of 20 dB per decade, which gives the desired phase margin.

Ideal conditions versus real world

Achieving these ideal conditions does not always happen in the real world. So, here’s an example that involves the control-to-output gain at +20 dB. The outcome is quite different, even if the same rules are applied as in the previous example and the effect of the +1 term in the gain equation is ignored.

The difference is that the gain of the TL431 and optocoupler, as configured, can never fall below that of the optocoupler alone because of the +1 term. That’s because the signal being sensed by the TL431 is also present on the voltage source providing the current into the optocoupler, hence the hidden loop. As the TL431 gain drops below zero dB, it becomes a very stable voltage. However, any signal on the voltage source (+VOUT in Figure 1) still results in a signal in the current through the optocoupler.

Choosing R3 to be equal to one-tenth of R1 means that if a designer had a 10 kHz 100 mV sine wave signal on the +Vout point of the circuit shown in Figure 1, it appears as a 10 mV signal on the TL431 cathode 180 degrees out-of-phase with the +VOUT signal. This design results in a 110 mV signal across the R4 resistor (100 mV from the + VOUT side of the resistor and 10 mV from the TL431 cathode). The circuit needs a 10 mV signal to have a zero dB gain at 10 kHz. The result is the total loop gain is still +20 dB at the desired crossover of 10 kHz.

As the frequency continues to increase, the error-amplifier output signal gets even weaker. However, the signal from the signal source remains the same and the current through the resistor R4 continues to be dominated by the voltage on +VOUT.

This means that as the error amplifier’s gain goes through zero dB, the gain of the feedback loop, comprising the TL431 and the optocoupler circuit, flattens out and becomes fixed at one or zero dB, as shown in Figure 4 (dotted line).

Figure 4. Gain components control-to-output, feedback network, total open-loop gain. Courtesy: Texas Instruments

The solution is to put a filter between R4 and VOUT, so that the voltage source for R4 is a stable voltage. Figure 5 shows a typical application of a filter with a series regulator in this case.

Figure 5. Feedback loop with additional filtering. Courtesy: Texas Instruments

Adding this filter network results in the gain curves shown in Figure 6, and the desired gain curve of the TL431 is achieved.

Figure 6. Effects of adding a filter between R4 and VOUT. Courtesy: Texas Instruments

A demonstration circuit to show these effects of adding a filter was built and tested. Figure 7 shows the circuit used for the testing.

Figure 7. Test circuit. Courtesy: Texas Instruments

The circuit’s loop gain was measured by injecting a signal across R9 and measuring the voltage at two points. The first point to be measured was at the junction of R9 and R7.

Depending on which gain is being measured, the TLV431 gain or at the optocoupler’s output, the second point was connected to either the cathode of the TLV431 or the photo transistor’s emitter of the CNY17 when measuring the gain at the CNY17, respectively.

Figure 8 shows the gain-and-phase of the TLV431. Figure 9 shows the gain-and-phase at the emitter of the CNY17.

Figure 8. Gain at TLV431. Courtesy: Texas Instruments

Figure 9. Gain at CNY17. Courtesy: Texas Instruments

As these figures show, the dc gains are slightly different because the CNY17’s CTR is not one-to-one. In addition, there is a phase shift of 180 degrees. This corresponds to the inversion that comes from the polarity from the TLV431’s cathode to the photo transistor’s emitter.

The calculated gain-and-phase is shown in Figure 10 for the gain and Figure 11 for the phase. The solid line represents the calculated gain at the TLV431’s cathode. The dotted line represents the calculated gain at the photo transistor’s emitter. The CTR has been modified to reflect the measured CTR in the calculations. The gain is in actual values, not dB.

Figure 10. Gain of the test circuit. Courtesy: Texas Instruments

Figure 11. Phase of the test circuit. Courtesy: Texas Instruments

This series of scope pictures shows the gain at various frequencies taken during the measurements. Figures 12 and 13 demonstrate the relative changes of the gain.

Figure 12. Voltages at 10 Hz. Courtesy: Texas Instruments

Figure 13. Voltages at 50 Hz. Courtesy: Texas Instruments

The top trace is the signal being inducted differentially across R9 (A in Figure 7), and being measured at the junction of R9 and R7. The bottom trace is the signal being generated at the cathode of the TLV431 (B in Figure 7), and the middle trace is the voltage on the emitter of the optocoupler (C in Figure 7).

As observed, the signal’s phase relation on the optocoupler emitter is 180 degrees out-of- phase with the voltage on the TLV431 cathode. Another thing observed is that the TLV431 signal’s amplitude is slightly stronger than the optocoupler’s phototransistor emitter. This strength is from the CTR being less than one. Finally, observe that the amplitude of the 50 Hz waveforms for the TLV431 and the optocoupler is smaller at 50 Hz than at 10 Hz.

Figure 14. Voltages at 100 Hz. Courtesy: Texas Instruments

Figure 15. Voltages at 500 Hz. Courtesy: Texas Instruments

The gain continues to decrease as the frequency increases. However, according to the loop response, the optocoupler’s gain, or amplitude, should stabilize while the gain of the TLV431 should continue to decrease. According to the graph in Figure 10, this should occur at about 500 Hz.

The injected signal is increased for the next few scope pictures so that the effects can be easily observed.

Figure 16. Voltages at 1 kHz. Courtesy: Texas Instruments

Figure 17. Voltages at 5 kHz. Courtesy: Texas Instruments

The TLV431’s output continues to decrease as the frequency increases even further. At 5 kHz, the ripple is almost unseen at this scale. However, the size of the input signal and the output of the optocoupler is almost the same.

Figure 18. Voltages at 10 kHz. Courtesy: Texas Instruments

At 10 kHz, the voltage on the TLV431 appears to be nearly a straight line while the optocoupler’s output is still reflecting the input sine wave. These observations reflect the measured and calculated results already discussed above.

Filter voltage source

In the design of a dc/dc converter that uses this type of feedback, it is often necessary to filter the voltage source that provides the current to the optocoupler. This helps to remove this sneak path and to control the gain of the feedback loop with the components around the TL431.

Also read: Tips and tricks: Power conversion design help