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In this series of posts, I intend to explain to you intuitively how Linear Regulators work and also show you how to design them yourself. By going through this post and the next couple of posts, you will see how incredibly easy and intuitive it is to design simple, yet stable Linear Regulators.
Close the switch to start.
Let me start by explaining the basic structure of a linear regulator. It consists of a Series Pass Transistor (in this case an NPN BJT), an error amplifier (the Op Amp) and a voltage reference (in this case, a zener diode). The job of the error amplifier is to drive the BJT in such a way that the output voltage does not deviate from the expected (or set) voltage value. It does so by comparing the output voltage with a voltage reference (which is very stable, has very low temperature coefficient and high current independence). In this circuit, a 5V zener diode is used as a reference. A constant current source is used to feed the zener so as to ensure voltage stability (a zener diode is not an appropriate reference). The output voltage is monitored through a Feedback Network, the two 10k resistors in this case.
Now let us see how the circuit works. As soon as the switch is closed, a current starts flowing through the circuit. Since, initially, the value of the output voltage is zero, the voltage at the inverting terminal (the '-' terminal) is also zero. Remember, the voltage at the '-' terminal is equal to half the output voltage, since
V- = Vo * (R1/R1+R2) ...(1)
Putting R1 = R2 = 10k, we get
V- = Vo/2 ...(2)
Returning to the working, as the voltage at the '-' terminal is zero and the voltage at the '+' (the non-inverting terminal) is 5V, the output voltage of the Op Amp (the drive to the BJT and NOT the regulator output voltage) is
Voa = Av * ( (V+) - (V-) ) ...(3)
where Av is the gain of the amplifier. Putting Av = 100k, V+ = 5V and V- = 0V, we get Vd = 500kV. But this is not possible! The Op Amp's output is limited by the power supply voltage, in this case 15V, because of which the drive to the BJT is also 15V. Eqn 3 gives the relation between the Op Amp's input voltage and it's output voltage.
This results in the BJT turning Hard ON and a current starts flowing through the load (100ohm resistor) and through the output capacitor (10uF capacitor). The capacitor starts charging up and the current through the load also starts increasing (Remember, current and voltage can never rise instantaneously to the maximum value). Due to this, the output voltage (of the regulator) starts increasing steadily. When the output voltage starts approaching 10V, the voltage at the '-' terminal (equal to half the output voltage, see eqn 2) approaches 5V.
Now let us recall eqn 3. Since (V+) - (V-) (which the difference between the two input voltages) starts reducing, the output voltage Voa also starts decreasing. Re-writing eqn 3,
Voa = Gain * Input_Voltage_Difference
Since the input voltage difference decreases, it means that the output voltage is approaching the desired value (in this case, 10V) and Voa decreases, so the drive to the BJT is no longer the full 15V, but it attains a lower value that is enough to sustain the 10V output voltage. This is how such a Linear Voltage Regulator works. The Op Amp does all that it can to ensure that the voltages at the two terminals stay as close to each other as possible, with minimal deviation, thus ensuring the the regulator output voltage stays constant.
Now let us quickly derive the formula for the regulator output voltage. The golden rule of the Op Amp is, like I just mentioned, that the two input voltage are kept as close to each other as possible. Therefore,
V+ = V- ...(4)
From eqn 1, we know the expression of V- and from the circuit, we know the value of V+, which is 5V. Substituting these in eqn 4, we get
5 = Vo * (R1/R1+R2)
On rearranging the above equation, we get
Vo = 5 * (1 + R2/R1) ...(5)
On substituting the values of R2 & R1 (10k each), we get Vo = 10V.
The 5V that you see in equation 5 is called reference voltage, or Vref for short. It is a variable and can be chosen as per convenience. On replacing 5V with the variable Vref in eqn 5, we get a more general formula
Vo = Vref * (1 + R2/R1) ...(6)
Equation 6 is a very powerful equation, just like the golden rule of the Op Amp, so I urge you to remember it, as it is a universal formula for all voltage regulators, be it a simple DIY Linear Regulator or a commercial Switching Regulator IC. It works everywhere.
If you made it all the way to the end of the description, you have learnt a lot about the fundamentals of pretty much all kinds of regulators (yes, even switch mode) and you can go on to learn about more advanced regulators. In my upcoming posts, I will show you how to design more advanced linear regulators. Thank you for reading:)
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