High Pass Filter
High Pass Filters
A High Pass Filter or HPF, is the exact opposite to that of the
previously seen Low Pass filter circuit, as now the two components have been interchanged with
the output signal ( Vout ) being taken from across the resistor as shown.
Where the low pass filter only allowed signals to pass below its cut-off frequency point,
ƒc, the passive high pass filter circuit as its name implies, only passes signals
above the selected cut-off point, ƒc eliminating any low frequency signals from
the waveform. Consider the circuit below.
The High Pass Filter Circuit
In this circuit arrangement, the reactance of the capacitor is very high at low frequencies so
the capacitor acts like an open circuit and blocks any input signals at Vin until the
cut-off frequency point ( ƒc ) is reached. Above this cut-off frequency point
the reactance of the capacitor has reduced sufficiently as to now act more like a short circuit allowing all of the
input signal to pass directly to the output as shown below in the High Pass Frequency Response Curve.
Frequency Response of a 1st Order High Pass Filter.
The Bode Plot or Frequency Response Curve above for a High Pass filter is the exact opposite
to that of a low pass filter. Here the signal is attenuated or damped at low frequencies with the output increasing at
+20dB/Decade (6dB/Octave) until the frequency reaches the cut-off point ( ƒc )
where again R = Xc. It has a response curve that extends down from infinity to the cut-off
frequency, where the output voltage amplitude is 1/√2
= 70.7% of the input signal value or -3dB (20 log (Vout/Vin)) of the input value.
Also we can see that the phase angle ( Φ ) of the output signal
LEADS that of the input and is equal to +45o at frequency ƒc. The
frequency response curve for a high pass filter implies that the filter can pass all signals out to infinity. However in
practice, the high pass filter response does not extend to infinity but is limited by the electrical characteristics of the
The cut-off frequency point for a first order high pass filter can be found using the same equation as
that of the low pass filter, but the equation for the phase shift is modified slightly to account for the positive phase
angle as shown below.
Cut-off Frequency and Phase Shift
The circuit gain, Av which is given as Vout/Vin (magnitude) and is calculated as:
Calculate the cut-off or "breakpoint" frequency ( ƒc ) for a
simple high pass filter consisting of an 82pF capacitor connected in series with
a 240kΩ resistor.
Second-order Low Pass Filter
Again as with low pass filters, high pass filter stages can be cascaded together to form a
second-order (two-pole) filter as shown.
Second-order High Pass Filter
The above circuit uses two first-order high pass filters connected or cascaded together to form
a second-order or two-pole filter network. Then a first-order high pass filter can be converted into a second-order type
by simply using an additional RC network, the same as for the 2nd-order low pass
filter. The resulting second-order high pass filter circuit will have a slope of -40dB/decade (-12dB/octave).
As with the low pass filter, the cut-off frequency, ƒc is determined
by both the resistors and capacitors as follows.
High Pass Filter Summary
The High Pass Filter is the exact opposite to the low pass filter. This filter has
no output voltage from DC (0Hz), up to a specified cut-off frequency ( ƒc ) point.
This lower cut-off frequency point is 70.7% or -3dB (dB = -20log Vout/Vin) of the voltage
gain allowed to pass. The frequency range "below" this cut-off point ƒc is generally known
as the Stop Band while the frequency range "above" this cut-off point is generally known as the Pass Band.
The cut-off frequency, corner frequency or -3dB point of a high pass filter can be found using the
standard formula of: ƒc = 1/(2πRC). The phase angle of the resulting output signal
at ƒc is +45o. Generally, the high pass filter is less distorting than
its equivalent low pass filter due to the higher operating frequencies.
A very common application of a passive high pass filter, is in audio amplifiers as a coupling capacitor
between two audio amplifier stages and in speaker systems to direct the higher frequency signals to the smaller "tweeter"
type speakers while blocking the lower bass signals or are also used as filters to reduce any low frequency noise or
"rumble" type distortion. When used like this in audio applications the high pass filter is sometimes called a
"low-cut", or "bass cut" filter.
The output voltage Vout depends upon the time constant and the frequency
of the input signal as seen previously. With an AC sinusoidal signal applied to the circuit it behaves as a simple 1st
Order high pass filter. But if we change the input signal to that of a "square wave" shaped signal that has an almost
vertical step input, the response of the circuit changes dramatically and produces a circuit known commonly as an
The RC Differentiator
Up until now the input waveform to the filter has been assumed to be sinusoidal or that of a sine wave
consisting of a fundamental signal and some harmonics operating in the frequency domain giving us a frequency domain response
for the filter. However, if we feed the High Pass Filter with a Square Wave signal operating in the
time domain giving an impulse or step response input, the output waveform will consist of short duration pulse or spikes as shown.
The RC Differentiator Circuit
Each cycle of the square wave input waveform produces two spikes at the output, one positive and one
negative and whose amplitude is equal to that of the input. The rate of decay of the spikes depends upon the time
constant, ( RC ) value of both components, ( t = R x C )
and the value of the input frequency. The output pulses resemble more and more the shape of the input signal as the frequency