Ⅰ Introduction
A highpass filter (HPF), also called a lowcut filter or basscut filter, passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. That is, unnecessary lowfrequency components or lowfrequency signal interference are removed. Highpass filters use the same two topologies as the lowpass filters: SallenKey and MFB. The only difference is that the positions of the resistors and the capacitors have changed. In other words, Highpass filters are complementary to lowpass filters.
Figure 1. High Pass RC Filter Circuit
Catalog
3.1 Passive Highpass Filter and Active Highpass Filter 3.2 Firstorder Highpass Filter and Secondorder Highpass Filter 
Ⅱ Highpass Filter Basic
2.1 Terminology
A highpass filter is a combination device of capacitors, inductors, and resistors that allows signal components above a certain frequency to pass through and greatly suppress signal components below that frequency. Its characteristics can be described in time domain and frequency domain by impulse response and frequency response respectively. The latter is represented by a function whose frequency is an independent variable. The latter is a function representation of frequency as an independent variable, which is generally a complex variable function with complex variable jω as an independent variable, expressed as H (jω). The H(ω) and amplitude φ(ω) are functions of angular frequency ω, which are called the "amplitudefrequency response" and "phasefrequency response" of the system, respectively. They show the signal components of different frequencies in the excitation source through the amplitude and phase changes encountered in this system. It can be proved that the "frequency response" of the system is the of the "impulse response" of the system, based on the Fourier Transform. When a linear passive system can be represented by an Norder linear differential equation, the frequency response H (jω) is a rational fraction, and its numerator and denominator correspond to the right and left sides of the differential equation, respectively.
2.2 Highpass Filter Circuit
Basic highpass filters are constructed using resistors with capacitors or inductors. The highpass filter composed of resistors and capacitors is called a highpass RC filter, and the highpass filter with resistors and inductors is called a highpass RL filter.
Figure 2. Simple Passive High Pass RC Filter Circuit
2.2 Cutoff Frequency
Generally, the cutoff frequency of the filter refers to the right frequency point of the lowpass filter passband and the left frequency point of the highpass filter passband, that is, the frequency response point of the filter. Usually defined by 1dB or 3dB relative loss point. For a highpass filter, its cutoff frequency is that frequency at which the output (load) voltage equals 70.7% of the input voltage (source). The highpass filter is based on the insertion loss at a sufficiently high passband frequency without parasitic stopband.
Figure 3. High Pass Filter Cutoff Frequency
Ⅲ Highpass Filter Types
The following two classification methods are independent of each other. Active highpass filters are more common, such as firstorder active highpass filters and secondorder active highpass filters.
3.1 Passive Highpass Filter and Active Highpass Filter
According to the different part devices, it can be divided into passive highpass filter and active highpass filter.
 Passive highpass filter
A kind of filters composed of passive components (resistor R, inductor L, and capacitor C), which is constructed using the principle that the reactance of capacitors and inductive components changes with frequency. The advantages of this type of filter are: the circuit is relatively simple, no DC power supply is required, and the reliability is high. The disadvantages are: the signal in the passband has energy loss, the load effect is more obvious, and electromagnetic induction is easily caused when using inductive components. When L is large, the volume and weight of the filter are relatively large, and it is not suitable in the low frequency domain.
 Active highpass filter
A filter consists of passive components (usually R and C) and active devices (such as integrated operational amplifiers). The advantage of this type of filter is that the signal in the passband has no energy loss, but also can be amplified, the load effect is not obvious, and the mutual influence is small when the multistage cascade is connected. It is easy to form a highorder filter using the simple method of cascade, and the filter is small, light, and does not require magnetic shielding (because no inductive components are used). The disadvantage is that the passband range is limited by the bandwidth of active devices (such as integrated op amps) and requires a DC power supply, and reliability is not as high as the passive filters, thus it is not suitable for high voltage, high frequency and high power.
Figure 4. LM741 Active Highpass Filter Circuit
3.2 Firstorder Highpass Filter and Secondorder Highpass Filter
According to the mathematical characteristics, it is divided into a firstorder highpass filter and a secondorder highpass filter, thirdorder highpass filterand so on.
Figure 5. Circuit Diagrams of Highpass Filter
 First Order High Pass Filter
The first order highpass filter requires a capacitor with a very high capacity, which causes very high fundamental losses, and therefore, it is rarely used.
Figure 6. Firstorder Highpass Filter
The derivation process is as follows: CV = Q (C represents capacitance, V voltage, Q electric quantity)
Loop current
，
where
Laplace transform:
Differential form:
,
 Secondorder High Pass Filter
The secondorder highpass filter has the best performance, but causes higher fundamental losses compared with the other type. The secondorder filter means that the filter contains the secondorder differential in the time domain expression, or the highest order of s of the transfer function denominator is 2, and the gain of the filter to DC component is 1.
Secondorder High Pass filter Circuit (voltage controlled)
Figure 5. Secondorder High Pass filter Circuit
Passband gain:
Transfer function:
Frequency response:
where, the expressing formula can be found
Conclusion: When f is less than f_{0}, the slope of the amplitudefrequency characteristic curve is + 40dB / dec; when Avp is greater than or equal to 3, the circuit selfexcited.
 Multichannel feedback highpass filter
Figure 6. Multichannel Feedback Highpass Filter
Voltage transfer function of this circuit:
Relationship between circuit parameters and components:
This circuit is designed with equal capacitance, that is, let C2 = C3 = C, C1 =  K  C, there is
Ⅳ Highpass Filter Transfer Function
 How to determine the transfer function of each highpass filter
The highorder filter consists of a cascade of secondorder filter sections and firstorder filter sections, and each filter section has a specific transfer function. In addition, the cutoff frequency and quality factor Q should be determined for the secondorder filter sections, and for the first order sections, only the cutoff frequency is to be determined.
 The general form of voltage transfer function of secondorder highpass filter:
Wc is the cutoff frequency, and the amplitudefrequency characteristic around the cutoff frequency is closely related to Q. K is the passband gain, which is the amplification factor when the frequency tends to infinity in the highpass filter.
 The general form of voltage transfer function of firstorder highpass filter:
The meaning of Wc and K is the same as that of the secondorder highpass filter, but there has no Q value.
When designing and calculating, to determine these parameters, it is necessary to check the normalized pole table of the filter to complete it through a certain conversion. (Whether a lowpass, highpass, bandpass, or bandreject filter, its frequency characteristics can be obtained by frequency coordinate transformation of the lowpass filter, so the lowpass filter also called a original filter.)
Figure 7. Highpass Filter Block Diagram
A common voltagecontrolled voltage source highpass filter circuit is used as an example. Its circuit diagram and voltage transfer function are as follows:
Figure 8. Voltagecontrolled Highpass Filter Circuit
Comparing this formula with the general expression of the transfer function of the secondorder highpass filter, we can know the cutoff frequency in the voltagecontrolled voltage source highpass filter circuit:
Ⅴ Highpass Filter Order
How to determine the order of the highpass filter
The order of Butterworth high pass filter is
Where n represents the order of filter, F_{C} is the cutoff frequency of  3dB, F_{2} is the frequency of a specified attenuation within the transition band, and A_{2} is the attenuation at F_{2}.
The order of Chebyshev high pass filter is:
Where n is the filter order, fc is the equal ripple cutoff frequency, a1 is the gain fluctuation (dB) in the passband, f2 is the frequency of a specified attenuation in the transition band, and a2 is the attenuation at f2 Volume (dB).
The fc in the above formula represents the equalripple cutoff frequency, that is, the frequency of attenuation in the transition zone at a_{1}. If the 3dB cutoff frequency is used in the design, it must be converted to an equal ripple cutoff frequency to get the above formula. The following table shows the proportional relationship between the cutoff frequency such as the Chebyshev highpass filter and the 3dB cutoff frequency.
Table 1: Ratio FC / f3db of equal ripple bandwidth to  3dB bandwidth of Chebyshev high pass filter
n 
2 
3 
4 
5 
6 
a1=0.1dB 
1.9432 
1.3690 
1.2131 
1.1347 
1.0929 
a1=0.2dB 
1.6743 
1.2835 
1.1564 
1.0992 
1.0685 
a1=0.5dB 
1.3897 
1.1675 
1.0931 
1.0593 
1.0410 
a1=1dB 
1.2176 
1.0949 
1.0530 
1.0338 
1.0234 
The highorder active highpass filter is formed by cascading several secondorder highpass filters (firstorder highpass filters should be added for oddorder ones). Each filter is called a filter section, and each has its own independent and Q value. The filter formed after the cascade can constitute different types of filters, such as Butterworth filter and Chebyshev filter.
 Calculation of firstorder highpass filter section:
 Calculation of secondorder highpass filter section:
Ⅵ Difference between Highpass Filter and Lowpass Filter
The difference between a highpass filter and a lowpass filter is that a highpass filter allows highfrequency or AC component signals to pass and suppresses lowfrequency or DC components. A lowpass filter is a filter that allows lowfrequency or DC components in a signal to pass through and suppress highfrequency components or interference and noise. In general, the lowpass filter retains signals that are smaller than the cutoff frequency, while the highpass filter retains signals that are larger than the cutoff frequency.
Ⅶ Highpass Filter Application
1) In the power system, a highpass filter is used to filter out harmonics of a certain order and above during harmonic compensation.
2) In audio system
The most overlooked and most useful EQ tool is the highpass filter, which can remove unwanted lowfrequency noise from the audio source. The highpass filter can be a part on the EQ equalizer, or it can be an independent plugin or device. Usually our speakers, mixers or microphones are equipped with highpass filters, because the lowcutting of the recorded human voice can make it easy to distinguish the noise, although this type of noise is very low and difficult to detect. For example, in most musical instruments, the highpass filter is used to cut off the sound lower 100Hz. You will find that the sound work is miraculously clean, but this does not apply to lowfrequency instruments such as kick drums and bass.
Ⅷ Question Related to Highpass Filter and Going Further
7.1 Question
What is the bandwidth of high pass filter?
7.2 Answer
The bandwidth of the filter denotes the value of frequency from which signals are allowed to pass. For example, if the bandwidth of the high pass filter is given as 50 kHz it means that only frequencies from 50 kHz to infinity are allowed to pass.
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