relationship between input and output voltage of power booster circuit

[khatus]

This is a power booster circuit. Here Q1 is a power transistor. I want to determine the relationship between input voltage(Vin) and output voltage (vout) here. and also want to determine Vout.



I have found that,



Here is my simulation. If the input voltage Vin = 15 volt The output voltage is fixed at = 13.28 volt i.e vout = 13.28. The VCC of transistor is 30 volt i.e VCC= 30 volt.the output voltage Vout is independent of transistor collector voltage i,e VCC. And if we increase the VCC from 30 volt to 50 volt the whole increased voltage (50V -30V = 20V)  is dropped across VCE of transistor Q1.
 


Please derive me the relation between Vin and vout. how 15 volt inputs give 13.28 volt output voltage. Please show me the calculation.

[tooki]

Normal op-amps need headroom between the supply voltage and the output. So if you’re only supplying the op-amp with +15V, its output will never reach +15V. Try giving it 17-20V.

There are so-called “rail to rail” op-amps that can swing more or less to the supply voltages.

[Zero999]

The simulation results are correct.

The op-amp is powered off 15V and its output can only swing to within 1V of its positive supply, which limits its output voltage to around 14V.

Q1 is an emitter follower, which only boosts the current, not voltage. The emitter voltage is always about 0.7V less than the base voltage.

This is why the output voltage saturates at about 13.3V.

If you reduced V_IN to 1V, then the circuit would work properly and the output voltage would be 11V.