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VCO using TL431 voltage reference

22 Oct 2013  | R O Ocaya

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Figure 3 shows in block schematic form how sustained oscillations start and build up when the internal equilibrium of the TL431 device is disturbed. The capacitor charges from a small, almost constant current that is derived from supply current I1. In figure 1, this charging current is denoted by I3. When the capacitor passes the equilibrium value of VREF, current I2, which is the combined collector currents of Q7 and Q8 in figure 2, rapidly flows and effectively siphons off charge stored in the capacitor. The duration of I2 is brief, but is sufficient to drop the capacitor voltage below the equilibrium again. The capacitor then begins to charge from I1 again, and the cycle attains steady oscillation. Since the discharge of the capacitor occurs very briefly, the current during discharge is very much larger than source current I1, according to I=ΔQ/Δt, where ΔQ is the charge acquired by the capacitor during its charging phase.


Figure 3: Simple illustration of the current paths in the TL431 relaxation oscillator.


Estimation of charging and discharging times
Since the charging and discharging currents are known, approximate expressions for the charge acquired during charging, and the charge dumped into the output stages of the TL431, can be found. The two expressions are equal during stable oscillation, a process akin to a two step bucket brigade. That is, charge acquired during charging equals charge lost during discharging. In figure 1,

I3 = I1—IBIAS

The magnitude of IBIAS in the TL431 is about 260µA over a wide range of VCTRL.

From first principles, the following differential equation results:


The resistance Rs is the series resistance connected to the control voltage. Solving the differential equation from the lower threshold to the upper threshold of VC during stable oscillation gives the charging time as


The discharge time is slightly more complex to estimate because the discharge occurs through a dynamic resistance. The effective resistance through which the acquired charge is dumped during discharge can be estimated as follows. Simulations and experiments show that during stable oscillation, VKA does not fall below about 1.60V or exceed about 2.74V. An inspection of the TL431 datasheet, figure 1, shows how, like a diode, the device exhibits dynamic resistance.


Figure 4: Characteristic of the TL431B showing dynamic resistance. Reproduced from [1].


This is a diode-like forward bias characteristic that can therefore be approximated by the function


Unlike normal junction diodes, the TL431 current has no significant temperature coefficient since it is designed around a band gap reference. The dynamic resistance can be shown to be


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