# Passive High Pass Filter : Circuit, Working, Types, Transfer Function & Its Applications

A high pass filter is an electronic filter that allows signals with a higher frequency than a certain cut-off frequency & attenuates signals by lower frequencies than that cut-off frequency. This filter is inverse to the low pass filter and is also known as HPF, bass-cut filter, or low-cut filter. The combination of low pass filter and high pass filter is known as band pass filter which allows only frequencies in a specific range. There are different kinds of high-pass filters based on the design of the circuit as well as components utilized to design a filter like; active high-pass filter, passive HPF, RC HPF, first-order HPF, second-order HPF, Butterworth, Chebyshev and Bessel high pass filters. This article briefly explains a passive high pass filter, its circuit, working, types, and applications.

## What is a Passive High Pass Filter?

A type of electronic filter used to allow high-frequency signals only to pass throughout while blocking low-frequency signals is known as a passive high-pass filter. This filter is also known as a passive filter because it doesn’t need an exterior power source for operation and also it depends exclusively on the incoming signal energy.

This filter is designed with passive components like; resistors, inductors & capacitors. These component values simply decide the filter’s cut-off frequency, where this frequency is below the signals that are blocked or attenuated.

### Passive High Pass Filter Circuit

The passive High pass filter design circuit is shown below which uses a resistor and a capacitor. This circuit is similar to the Passive LPF but the resistor and capacitor are simply interchanged within the circuit. The capacitor in a passive high-pass filter circuit is connected simply in series by the resistor. Generally when an input signal is provided to the series combination of a non-polarized capacitor & resistor then the filtered output is available or drawn across the resistor.

This filter simply allows the higher frequencies & blocks the lower frequency signals. The cut-off frequency value mainly depends on the values of components selected for the design of the circuit. These filters have several applications at a 10 MHz high-frequency range. Because of the components interchange within this circuit, the responses by the capacitor delivered will change which are opposite exactly to the low pass filter response.

The capacitor in this circuit at the low frequencies performs like an open circuit and at higher frequencies; it acts like a short circuit. In this circuit, the capacitor blocks the lower frequencies that enter into the capacitor because of the capacitor’s capacitive reactance.

The capacitor opposes some amount of current in this circuit to bind in the capacitor’s capacitance range. So the capacitor after the cut-off frequency permits all the frequencies due to the capacitive reactance reduction value. So this makes this filter circuit pass the whole input signal to the output whenever the frequency of the input signal is higher as compared to the cut-off frequency ‘fc’.

The value of reactance increases at lower frequencies then the capacity to resist the flow of current throughout the capacitor is enhanced. The frequency band under the cut-off frequency is called as ‘Stop Band’ & the frequency band after the cut-off frequency is called the ‘Pass Band’.

#### Cut-off frequency

The formula for the cut-off frequency for the passive high pass filter is shown below. This formula is similar to the low-pass filter.

**Fc = 1 / 2πRC**

Where ‘R’ is resistance & ’C’ is capacitance.

#### Phase Angle of Passive High Pass Filter

The phase angle of passive HPF is denoted with φ (Phi) which will be +45 at the output as of i/p signal at -3dB (or) Cut-off frequency.

According to the filter’s frequency response, it passes all signals over the cut-off frequency to infinity. The Phase shift formula is not similar to a low pass filter because, in this filter, the phase will become negative, although in HPF it is a positive phase shift, thus the phase angle formula is;

**Phase shift (φ) = arctan (1/2πfRC)**

#### Time Constant

The capacitor in the circuit gets a charging & discharging effect from the frequencies of the input signal is known as the Time Constant which is denoted with τ (Tau). The time constant is also related to cut-off frequency.

**τ = RC = 1 / 2πfc**

Sometimes whenever we have the value of time constant, we have to know the cut-off frequency, so by changing the formula we can get the below equation.

**fc = 1 / 2πRC**

**We know that τ = RC**

**So, the above equation will become fc = 1 / 2πτ.**

#### Example

The active high pass filter circuit using a 330k resistor and 100pF capacitor is shown below. Calculate the cut-off frequency.

The formula to calculate the cut-off Frequency is shown below.

Cut off frequency fc = 1/2πfC

We know that resistor 330k and capacitor 100pF values, substitute these values in the above equation.

Cut off frequency fc = 1/2 x 3.14 x 330000 x 100 x 10^-12.

fc = 4825Hz (or) 4.825Khz.

#### Passive High Pass Filter Transfer Function

The transfer function explains the main relationship between the input & output signals of the passive high-pass filter. So, the transfer function of passive HPF calculation is discussed below.

Vin = IZ

Vin = I (R + 1/jωC)

Vo = IR

Vo/ Vin

IR/ I (R + 1/jωC)

Vo/ Vin = RjωC / R jωC + 1)

Take RC = 1/ωC

Vo/ Vi = j(ω/ωC)/ j(ω/ωC) + 1

Vo/ Vin = j(ω/ωC)/√ j(ω/ωC)^ 2 + 1

The above equation is a passive high-pass filter transfer function. So, the voltage gain at every ‘ω’ value of a filter can be measured with the above equation.

## Types of Passive High Pass Filters

There are two types of passive high pass filters; first order passive HPF and second order passive HPF which are discussed below.

#### First-order Passive HPF

The first-order passive high-pass filter circuit is shown below. This circuit can be designed with only one reactive component with a resistor. This filter circuit blocks low-frequency signals but allows the high-frequency signals above the set value. This circuit uses passive components and doesn’t need any external power source. Whenever an input signal is provided to this series combination of capacitor & resistor then the filtered output will be obtained across the resistor.

The Cut-off frequency formula for first-order passive HPS is the same as the passive low pass filter which is shown below.

**fc = 1 / 2πRC**

#### Second Order Passive HPF

The second-order passive high-pass filter circuit is shown below. This filter circuit is designed by cascading two first-order HPFs. This circuit uses two reactive components two capacitors and two resistors which makes the filter circuit second order. So this two-stage filter performance is equivalent to a single-stage filter although the slope of this filter can be obtained at -40 dB/ decade due to the variation within cut-off frequency.

This filter is very efficient as compared to a single-stage filter because it includes two storage points. So, the cut-off frequency for a two-stage filter mainly depends on the two capacitors & two resistors values which are given as;

fc = 1/ (2π√(R1*C1*R2*C2)) Hz

### Applications

The **applications of passive high-pass filters** include the following.

- A passive High Pass Filter is a filter that will block Low frequencies, but pass the high frequency above the predetermined value.
- Passive high-pass filters are used in equalizers & audio receivers.
- These are used in music control systems & frequency modulation.
- These are used in function generators, pulse generators, ramp-to-step generators, CROs, CRTs, etc.
- These filters are used normally in audio processing for removing low-frequency noise in audio amplifiers wherever maximum frequencies are required.
- These filters are used frequently in HPFs for enhancing the edges as well as other higher-frequency components within digital images.
- These are used in different industrial & also scientific applications like; seismic analysis, and radar systems & within the biomedical field to understand ECGs.
- These types of filters are crucial tools within electronics & signal processing to allow high-frequency signals to allow and block low-frequency-based signals.

Thus, this is an overview of a passive high-pass filter, circuits, working, types, and its applications. A filter circuit is designed with only passive components like; resistor & capacitor. These filters do not require any exterior source so they have no gain which means the amplitude of the output signal is equivalent always or below the amplitude of the input signal. These filter designs are extremely simple and the components used to make these filters are also very cheap. Here is a question for you, what is a passive low pass filter?