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イノベーション・フォーラム

A single capacitor is enough, don’t add that RC! 

 著者: Christophe Basso - 2014-06-26 14:37:31.0

I often review electrical schematics in my daily job. Sometimes it is because a failure occurred in production and design integrity may be questioned, but most of the time, I am consulted on the power converter architecture, before production is launched. People expect me to report any particular flaw I can spot such as an overlooked important parameter for instance. Usually, technical discussions start around power (design margins, safety and so on) and slowly deviate towards different subjects. Loop control is one of them and, in particular, the TL431 usage in the isolated compensation path.

The TL431 is an interesting 3-leg animal, packing a reference voltage together with an operational amplifier (op amp). It is basically an open-collector op amp sinking current between cathode and anode when its reference pin exceeds 2.5 V. Coupled with an optocoupler, it is found in almost every ac-dc notebook adapter sold on the market these days. Despite its popularity, numerous designers still configure the part like a compensated op amp as shown below.

Figure 1

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1: Designers often associate a traditional op amp-based type 2 network with a TL431

 

If this association of passive elements is not wrong per se, it reflects a misconception of the circuit operation. In particular, the presence of a fast lane through resistor R20. By fast lane, I mean the fact that the LED current – which closes the feedback loop – does not only depend on the TL431 operation but also directly on Vout via R20. And that is the difficulty here: at high frequency, when C9 impedance is low, the TL431 ac current no longer depends on information brought by R22, the output voltage sensing network. So you expect a zero-current ac modulation in the LED imposed by the sensing network, nicely rolling off the gain. Unfortunately, as the TL431 cathode voltage is maintained in dc (like a programmable Zener diode), if Vout changes, the ac current in the LED undergoes modulation through R20: this is the fast lane effect, canceling the gain roll-off at high frequency as you would expect from an op amp-based type 2 circuit.

Actually, when implementing the Figure 1 sketch, the designer expects to calculate elements values as with a type 2 compensator built around an op amp. However, because of the fast lane contribution, the transfer function totally differs as expressed by the simplified below low-Q definition:

Equation 1

 

 

 

 

(1)

 

As indicated, there are 3 poles and 2 zeros, not really the classical type 2 you want (2 poles and 1 zero). In the above expression, if we consider C9 smaller than C10 and R2 smaller than R22 then the poles and zeros are approximately located here:

Equation 2(2)

In this expression, C2 is the sum of the added capacitor C6 and the optocoupler parasitic capacitance Copto. If wz1 and wp1 are closely located, they cancel each other and the transfer function simplifies to another type 2 expression:

Equation 3 (3)

To verify our results, it is interesting to implement the circuit in SPICE and confront the ac response with that of a mathematical solver such as Mathcad® for instance. This is what Figure 2 shows you, with the following component values:

 

Rpullup = 20 kΩ, R22 = 38 kΩ, R20 = 1.8 kΩ, C9 = 470 pF, C2 = 2.3 nF, CTR = 30%, C10 = 10 nF and R2 = 15 kΩ.

 

With these values, the poles and zeros are located at:

 

fz1 = 32.2 kHz, fz2 = 293 Hz, fp1 = 22.5 kHz and fp2 = 3.4 kHz

 

The boost in phase occurs at the geometric means of fz2 and fp2 which is 998 Hz. It is confirmed by the phase boost taking place at this frequency.

Figure 2

Figure 2: Perfect matching between the SPICE simulation and the equation-based approach

 

So yes, this is a type 2 response but you can obtain exactly the same response without the usage of the C10R2 network. A single capacitor connected between the TL431 cathode and the reference pin will not only introduce an origin pole, it will also produce a zero thanks to the fast lane action. The simpler schematic appears in Figure 3.

Figure 3

Figure 3: The right way to build a type 2 compensator with a TL431 requires a single capacitor

 

In conclusion, rather than compensating the TL431 as you would do with an op amp, it is best to capitalize on the fast lane presence and understand its role. When you do that, you realize that a single capacitor can do the job. This is the correct way to build a type 2 compensator with a TL431 and optocoupler. More details on how to design the compensator are given in Ref. 1.

____________________________________________________________________________________________________ 

 

Reference

 

  1. Christophe Basso, “Designing Control Loops for Linear and Switching Power Supplies – A Tutorial Guide”, Artech House, Boston 2012, ISBN 978-1-60807-557-7

 

 

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Rolhen Corros 2014-08-13 02:01:34.0 コメント・レーティング: Vote down 0 Vote up
Informative notes for TL431, not 3 leg animal but 3 leg monster. :) I always find it on every SMPS, on most known Brand /maker (and unknown - from china).

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