Low Pass Filter and High Pass Filter Circuits

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Topics Covered :
  • What is Capacitive Reactance ?
  • Using Ohm’s Law
  • Selecting Specific Frequencies
  • Low Pass Filters
  • High Pass Filters

1. What is Capacitive Reactance ?

There’s a very common difference between a resistor and a capacitor : 

  • In case of a resistor, the resistance value remains constant i.e. it doesn’t change even on varying the current or the voltage.
  • But unlike resistor, the value of capacitance depends on the current and voltage in the circuit.

We have already learnt about Charging and Discharging of Capacitor in the article : Learning about Capacitors . According to that, if our circuit consists of only a Capacitor attached to a battery, then :

  • Capacitor blocks the DC current except at the time of charging & discharging
  • Capacitor allows AC easily as it is nothing but a cycle of charging, discharging and recharging

Refer to the timeline diagram below which shows how resistance to electron flow is offered by capacitor during charging 

Timeline – Charging Capacitor

This resistance offered by a Capacitor is referred to as ‘Capacitive Reactance’

f –> represents the frequency of the source

Note that :

Case : DC Source is attached across capacitor

Result : We all know that frequency of DC Source is zero as there is no switching in polarity. Therefore, f=0 and we get reactance as infinite. Hence, we can see that the circuit almost behaves as an open circuit in case of a DC Source

And also in case of AC Source, it is quite evident from the formula that, if the frequency of the source is increased, it results in decrease of capacitive reactance. Let’s take 2 cases to understand this : Both are AC Source – One with f = 50kHz and second with f = 10Hz (Capacitance is 10uF)

                                 Sub-Case f = 50 kHz                                                  Sub-Case f = 10 Hz             


Hence, verified !

2. Using Ohm’s Law

  • It is possible to use Ohm’s Law in this case as well. Just consider the capacitive reactance as some kind of resistor and then apply Ohm’s Law on it.
  • But note that : Just one frequency at a time while using Ohm’s Law

Let’s calculate the peak current achieved in the circuits in the 2 examples considered in previous section-1 . Circuit has all the parameters same, just the peak voltage of AC Source is now given to be 5V


3. Selecting Specific Frequencies

This frequency dependent behaviour of capacitors makes them suitable to build some special type of circuits called Low Pass and High Pass Circuits.

  • Capacitors block DC and allow AC. But with the help of these filter circuits, we can control which AC signals will specifically be allowed to pass. Hence, we call them as filtering circuits

Just remember this analogy :

  • Getting a voltage somewhere is equivalent to getting a signal over there.

3.1 Low Pass Filters

To understand this circuits, lets take 2 cases : one at low frequency (f=0) and another at very high frequency. 

Fig. Low Pass Filter Circuit

We can find the relation,

Case 1 : Low Frequency (f = 0) of Source

This implies that the source behaves like a DC. And we know that, in steady state, Vc = Vout = Vin i.e. the whole source voltage comes across the capacitor 

Case 2: Very High Frequency of Source

At high frequency, the capacitive reactance is low –> This makes the capacitor to behave as short circuit–> This implies, there is no voltage drop across capacitor –> Therefore, Vc = Vout = 0

As discussed earlier, 

If we get a voltage at Vout –> It implies that we have the signal of that frequency over there. So, in case of above circuit, we are getting voltage at Vout in case of low frequency 

  • Hence, as the above circuit allows low frequency signals to pass (from input to output), the circuit is known as Low-Pass Filter

3.2 High Pass Filters

To understand this circuit, Again lets take the same 2 cases : one at low frequency (f=0) and another at very high frequency. 

Fig. High Pass Filter Circuit

Case 1 : Low Frequency (f = 0) of Source

This implies that the source behaves like a DC. And we know that, in steady state, Vc = Vin i.e. the whole source voltage comes across the capacitor. But Vout = 0 in this case, as Vout is now the voltage across the resistor (Therefore, Vout = VR = 0)

Case 2: Very High Frequency of Source

At high frequency, the capacitive reactance is low –> This makes the capacitor to behave as short circuit–> This implies, there is no voltage drop across capacitor –> Therefore, Vc = 0 . But, because of this, the whole source voltage shifts to the resistor. 

This makes VR= Vout = Vin

If we get a voltage at Vout –> It implies that we have the signal of that frequency at output. So, in case of above circuit, we are getting voltage at Vout in case of high frequency 

  • Hence, as the above circuit allows high frequency signals to pass (from input to output), the circuit is known as High-Pass Filter

Conclusion :

We have discussed the basics of the High and Low Pass Filter Circuits. The most fundamental difference between the two is the position of output voltage. 

  • In case of Low Pass Filters, Vout is set across the capacitor
  • While, in case of High Pass Filers, Vout is set across the resistor

Keep Learning !

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