# Rectifier output voltage in RC and LC choke input filters

Why does the choke input filter produce a DC output voltage equal to the average value of the rectified voltage given as input to this filter, while the capacitor input filter produces a DC output voltage equal to the peak value of the rectified voltage given as input to the filter?

Why is it so when both are supplied from the same rectifier?

• The choke input filter is "often" used in polyphase rectifiers which have an internal impedance "proportional" to that inductor. Sep 2 at 14:09

Why does the choke input filter produce a DC output voltage equal to the average value of the rectified voltage given as input to this filter,

There is a property of inductors that, once you understand it, makes analysis of circuits with inductors much easier. This property is known as inductor voltage balance (or inductor volt-second balance). If a circuit is in a periodic steady state, that is, the same cycle of states occurs over and over periodically, then the average voltage on one side of an ideal inductor is equal to the average voltage on the other. (Real inductors have resistance, and there is a voltage drop due to this resistance, so the inductor voltage balance described above is not exact for real inductors).

This is the derivation.

For an ideal inductor

$$V_L = -I_L'L$$

so over a cycle,

$$\int_0^T V_L dt = -\Delta I_L L = -L \Delta I_L$$

Since we have assumed the circuit is in steady state, $$\I\$$ returns to its original value, and so $$\\Delta I = 0\$$.

Thus

$$\int_0^T V_L dt = 0$$

which says that the average of $$\V_L\$$ over a cycle is 0.

Since the average voltage across the inductor is 0, the average voltage on one side of the inductor must equal the average voltage on the other side of the inductor.

And that means that in any filter of the form

simulate this circuit – Schematic created using CircuitLab

the average voltage at $$\V_{in}\$$ will equal the average voltage at $$\V_{out}\$$ if we assume that L1 is an ideal inductor (i.e. has no internal resistance).

the capacitor input filter produces a DC output voltage equal to the peak value of the rectified voltage given as input to the filter?

Consider this unregulated supply circuit:

simulate this circuit

Here are the input voltage, the absolute value of the input voltage, and output voltage.

And here is the current through the rectifier.

Notice that current only flows through the rectifier when the absolute value of the input voltage is greater than the output capacitor voltage. Put another way, the capacitor charges through the rectifier, but discharges through the load.

It is often a good approximation to say that a diode has a voltage drop of some fixed amount, say 0.65 V, when it is conducting. The voltage dropped by a bridge rectifier would then be 2 diode drops, or $$\\approx\$$ 1.3V.

Since the voltage drop through the rectifier is "fixed" when it is conducting, the maximum voltage of the capacitor will be this fixed amount less than the maximum (absolute value of the) voltage applied to the input of the rectifier. And that is why it is (more or less) correct to say that the peak output voltage of the unregulated power supply is equal to the peak input voltage (minus the rectifier voltage drop).

• So it means that because of this property the inductor takes only the average value of unfiltered rectified input and transfer it as it is to the input of capacitor in RC filter ? @Math Keeps Me Busy?
– Alex
Sep 2 at 17:46
• And because of the same reason peak voltage of the unfiltered rectified input will not apear at other end of the inductor i.e to the input of the capacitor and only the average value from the unfiltered rectified input will be transferred to the input of the capacitor?
– Alex
Sep 2 at 17:58
• I added a small bit to my answer. However, to be honest, I am a bit confused by your questions. In your first question do you mean "and transfer it as it is to the input of capacitor in LC filter" ? If so, yes. As far as the second question, the inductor voltage balance rule says nothing about the peak voltage across the inductor. The output peak voltage of an LC filter can be higher or lower, depending upon the frequency of input, and the values of the components (including the load). Sep 2 at 19:18