# I have a doubt with respect to capacitor's role in low pass and high pass filter.

#### Vikram50517

Joined Jan 4, 2020
81
Hello mates,
Sorry for the pretty inciting caption. I have a doubt with respect to capacitor's role in low pass and high pass filter. I came across many descriptions which stated that the main reason why a capacitor is able to block high pass freq components in a low pass filter is, it is not able to CHARGE AND DISCHARGE
within the timeframe of a high freq component signal and thus its response is 0 to those signals, but for low freq signal components, it is able to charge and discharge and reproduce them at the output.

Going by that Logic, if in a high pass filter, the capacitor faces the same high frequency signal components, then how is it able to allow the high frequency components?? How does it charge and discharge so fast in this case whereas it is not able to reproduce the same function in the case of a Low Pass Filter??

PS: Iam aware of the capacitor blocks DC and allows AC stuff, I just wanted to know how it acts as high pass when i think in terms of charging discharging way.

#### crutschow

Joined Mar 14, 2008
34,060
it is not able to CHARGE AND DISCHARGE
within the timeframe of a high freq component signal and thus its response is 0 to those signals
Where did you get that odd statement?
It's the resistor in series with the capacitor that determines the charge and discharge of the capacitor, not just the capacitor (R*C value).
The resistor limits the current to the capacitor, and that's what determines how much the capacitor charges and discharges in the period of the frequency-of-interest.

Look up RC time-constant.

#### Vikram50517

Joined Jan 4, 2020
81
Thanks a lot for the quick reply. Let me post the sources for the statement i claimed.
(In the first video, see from 1:00 to 3:00)
(This Second video in all, simulates how the capacitor is not able to respond to high frequency signals due to it unable to charge and discharge within the very small time frame the high freq signal has)

#### Ya’akov

Joined Jan 27, 2019
8,974
In a high pass RC filter, the capacitor is in series with the high side and resistor goes from the high side to ground.

The reactance of the circuit, which is based on the combination of the frequncy dependent resistance of the capacitor, and the resistance of the resistor is inversely proportional to the frequency applied.

So, the capacitor passes the high frequencies as it always does with little resistance but as the frequency decreases the reactance increases and those signals encounter increasing attenuation.

In the low pass RC filter, the resistor and capacitor switch positions with the resistor in series with the high side and the capacitor from the high to the low. The capacitor acts exactly as described offering high resistance to frequencies below the cut off and so having no effect on that as they pass through.

But, the capacitor has low resistance to frequencies above cut off so they are shorted to ground and don’t make it into the output signal.

Keep in mind the cut off frequency is a function of the values of the capacitor and resistor, so high- and low-pass are relative to that.

#### MrChips

Joined Oct 2, 2009
30,504
Charging and discharging properties of a capacitor is one way of studying its behavior. This method is used to analyze the time response of a capacitor to DC step voltages.

To understand the role of a capacitor in low-pass and high-pass filters it is better to understand reactance.
The reactance of a capacitor is measured in ohms and is a function of frequency.

The simple formula to remember is:

reactance Xc = 1 / ωC

where Xc is measured in ohms
C = capacitance in Farads
ω = angular velocity in radians/second

since there are 2π radians in each cycle,
ω =2πf
where f = frequency in Hz.

At very low frequencies the reactance is high and will appear as an open circuit to AC.
At very high frequencies the reactance is low and will appear as a short circuit to AC.

To understand the role of a capacitor in an RC filter, all you have to do is to look at a basic voltage divider.

Z in this diagram refers to impedance in ohms.

In a resistor voltage divider,
Vout = Vin x R2 / (R1 + R2)
This applies to both DC and AC circuits.

For an RC circuit, we apply the voltage divider formula using reactance for AC signals.

Vout = Vin x X2 / (X1 + X2)

The reactance of a resistor R is R ohms
The reactance of a capacitor is 1/2πfC ohms.

#### Vikram50517

Joined Jan 4, 2020
81
In a high pass RC filter, the capacitor is in series with the high side and resistor goes from the high side to ground.

The reactance of the circuit, which is based on the combination of the frequncy dependent resistance of the capacitor, and the resistance of the resistor is inversely proportional to the frequency applied.

So, the capacitor passes the high frequencies as it always does with little resistance but as the frequency decreases the reactance increases and those signals encounter increasing attenuation.

In the low pass RC filter, the resistor and capacitor switch positions with the resistor in series with the high side and the capacitor from the high to the low. The capacitor acts exactly as described offering high resistance to frequencies below the cut off and so having no effect on that as they pass through.

But, the capacitor has low resistance to frequencies above cut off so they are shorted to ground and don’t make it into the output signal.

Keep in mind the cut off frequency is a function of the values of the capacitor and resistor, so high- and low-pass are relative to that.
First of all, thanks a lot for your time and interest to respond to my query. I thoroughly understand your answer sir.

#### Vikram50517

Joined Jan 4, 2020
81
Charging and discharging properties of a capacitor is one way of studying its behavior. This method is used to analyze the time response of a capacitor to DC step voltages.

To understand the role of a capacitor in low-pass and high-pass filters it is better to understand reactance.
The reactance of a capacitor is measured in ohms and is a function of frequency.

The simple formula to remember is:

reactance Xc = 1 / ωC

where Xc is meausured in ohms
C = capacitance in Farads
ω = angular velocity in radians/second

since there are 2π radians in each cycle,
ω =2πf
where f = frequency in Hz.

At very low frequencies the reactance is high and will appear as an open circuit to AC.
At very high frequencies the reactance is low and will appear as a short circuit to AC.

To understand the role of a capacitor in an RC filter, all you have to do is to look at a basic voltage divider.

View attachment 262898

Z in this diagram refers to impedance in ohms.

In a resistor voltage divider,
Vout = Vin x R2 / (R1 + R2)
This applies to both DC and AC circuits.

For an RC circuit, we apply the voltage divider formula using reactance for AC signals.

Vout = Vin x X2 / (X1 + X2)

The reactance of a resistor R is R ohms
The reactance of a capacitor is 1/2πfC ohms.
Thanks a lot Mr Chips. The particular statement of yours "To understand the role of a capacitor in low-pass and high-pass filters it is better to understand reactance" clarified my query exactly i should say . Thank you
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