# Biasing the TL431 for Improved Output Impedance

Jan. 1, 2005
The TL431 is a well-known voltage reference integrated circuit used in Switch-Mode Power Supply (SMPS) feedback loops. Combining a reference voltage and

The TL431 is a well-known voltage reference integrated circuit used in Switch-Mode Power Supply (SMPS) feedback loops. Combining a reference voltage and an open-collector error amplifier, it offers advantages such as simplicity of implementation and low cost. Despite its widespread use in the industry, some designers still neglect to control the biasing current of the device with an external resistor, thereby degrading the final specification. Fig.1 shows the simplified schematic of a TL431 with a reference voltage and error amplifier driving an NPN transistor.

A power supply is a closed system where a fraction of the output voltage is compared to a reference, VREF in the TL431. A simplified dc model of an SMPS is a flyback topology where VOUT is compared to VREF via a resistive divider affected by a transfer ratio of α (Fig. 2). The theoretical voltage expected from such a configuration is simply VREF/α. Unfortunately, the entire gain chain and various impedances will affect this value. Writing the output voltage definition, where each Greek letter corresponds to a gain and RSOL to the open-loop output impedance:

VOUT = (VREF-αVOUT)(βG-RSOL)V OUT/RL Eq. 1

VOUT = VREFβG/(1+αβG+RSOL/RL) Eq. 2

The static error is defined by ε, which is:

ε = VREF/α-VOUT

or

ε = VREF(RSOL+RL)/α(RSOL+αβGRL+RL Eq. 3

From Equation 3, an increase in the gain β helps reduce the static error, which eventually affects the output voltage precision. Another important parameter influenced by the gain loop is the output impedance. The output impedance of a system can be calculated in different ways. Any generator can be reduced to its Thevenin equivalent; that is, a voltage source Vth (VOUT measured without any load — open circuit — or RL = ∞ in Eq. 2), followed by an output impedance Rth, that can be calculated. One option consists in calculating a resistor RL that, once wired between the output and ground, will reduce Vth to Vth/2. First, define a resistive divider with RL equal to Rth: Rth is the closed-loop output impedance, also called RSCL, to be found. That can be done quickly via Eq. 2, assuming RL = ∞:

Vth/2 = VOUT(RL), i.e. what value of RL will divide the Thevenin voltage by 2?

VREFβG/(1+αβG)/2 = VREFβG/(1+αβG+RSOL/RL)

RL = RSCL = RSOL/(1+αβG) Eqs. 4 & 5

Equation 5 illustrates the following:

• If the dc error amplifier gain, βdc is high, then RSCL is close to zero.

• Because the feedback return path β(p) is compensated, when the gain goes low with increasing frequency, RSCL starts to rise. A resistance whose value increases with frequency looks like an inductance.

• When the gain, β(p), has dropped to zero, then the system exhibits the same output impedance (RSOL) as when there is no feedback (i.e. system runs open-loop).

This is why most SMPS designers keep a large dc gain: first, to reduce the static error ε, and second, to reduce the dynamic output impedance of the converter. Here, the dc gain will be provided by the TL431. It can be wired in a shunt regulator configuration using an NCP1200 optocoupler between the input and output stages (Fig. 3).

Assume there is no Rbias resistor. First, calculate the divider network resistors Rupp and Rlower. To do this, select a bridge current Ib, greater than the TL431 reference pin bias current of 6.5 µA (max) to minimize the error incurred in Rupp because of this bias. Choose Ib = 1 mA for an output voltage of 12 V. Since the TL431 imposes 2.5 V across Rlow, then with a 1 mA current imposed by Rupp, Rlow becomes 2.5 V/1 mA = 2.5 kΩ. Then, Rupp simply equals 12 V- 2.5 V/1 mA = 9.5 kΩ.

Lower bias currents can be selected to reduce the standby power in no-load conditions. Once the bridge value is chosen, a value for RS is next. RSmust be able to deliver enough current to bring the optocoupler collector (or the feedback pin) below 1.2 V to initiate a skip cycle in no-load operations. Inside the NCP1200 optocoupler, there is an 8-kΩ pull-up resistor from pin 2 to an internal 5 V reference voltage. If the feedback current is 475 µA to bring pin 2 to 1.2 V (Vpin 2 = 5 - (475 µA × 8 kΩ), then, considering a worst-case Current Transfer Ratio (CTR) of 50% for the optocoupler, Rs must be smaller than (VOUT - 2.5 V- 1 V)/950 µA < 8.94 kΩ: elect it to be 8.2 kΩ. The 2.5 V comes from the fact that the minimum cathode-anode voltage cannot be lower than 2.5 V for the TL431 and there is a 1-V forward drop from the LED.

Keeping the 8.2-kΩ resistor in series with the TL431 and a CTR worst case of 150% (the opposite case of the previous one, meaning a smaller current is needed in the LED), then various scenarios can occur:

• Light load conditions: IFB = 475 µA, then IL = 475 µA/1.5 = 316 µA.

• Moderate load conditions, VFB = 2.3 V, IFB = 337.5 µA, then IL = 337.5 µA/1.5 = 225 µA.

• Heavy load conditions, VFB = 3 V, IFB = 250 µA, then IL = 250 µA / 1.5 = 166 µA.

This shows that the biasing current of the TL431 not only varies with the load current, but also with the optocoupler CTR. And there is nothing to be gained by reducing Rs, because what matters is the current inside the LED to fix the right feedback voltage on the controller side. The design issue in this case, comes from the TL431 data-sheet: You must inject more than a 1-mA biasing current to benefit from different guaranteed specs among which is the TL431 gain. If the TL431 is not properly biased, it will degrade the open-loop gain β of the previous equations: ε increases and RSCL increases.

Fortunately, a bias current can be imposed externally via the resistor Rbias. This resistor will be calculated in the worse case; that it to say at high load (and highest CTR) as exemplified by scenario 3 because the lack of current there is largest. In this situation, IL = 166 µA. Therefore, 166 µA (8.2 k) = 1.36 V is dropped over RS.

If 1 V is the LED forward drop, then the cathode voltage will be: 12 - 1.36 - 1 = 9.64 V. Knowing that VOUT is constant at 12 V, then imposing a 1-mA current via Rbias will lead to Rbias = (12 - 9.64) / 1 mA = 2.36 kΩ or 2.2 kΩ for a normalized value.

Therefore, impose a minimum current of 1 mA + 166 uA = 1.16 mA in the TL431. Under no-load conditions, the 316 µA of scenario 1 forces a 12 - (8.2 kΩ × 316 µA) - 1 = 8.4 V on the cathode, which leads to a total bias current flowing inside the TL431 of (12 - 8.4)/2.2 k = 1.63 mA plus the actual feedback current of 316 µA, which comes to 1.95 mA. This should be a safe value.

An experiment has been carried on a power supply built with a NCP1200 with and without the biasing resistor (here a 3.3 kΩ). Fig. 4 shows the effects of the resistor.

In the first case, without biasing element, the output impedance was measured to be 57 mΩ. By connecting the bias resistor, that value dropped to 4 mΩ.

In conclusion, do not forget to properly bias the TL431 via an external resistor. If an extra 1 mA is too high on the output (because the no-load standby power should be minimized), choose a TLV431 (VREF = 1.24 V) or a NCP100 (VREF = 0.7 V), because they only require a minimum bias current of 100 µA but exhibit lower breakdown voltages. Also, a series resistor RS of 8.2 kΩ is rare because this resistor combines with the optocoupler collector pull-up resistor to form a dc gain. Values around 1 kΩ or slightly higher are more typical values.