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High-Pass Filter Explained: Circuit Design, Types, Uses & Formulas

Electronic filters are crucial in signal processing, helping us isolate or suppress unwanted frequencies. One important category is the high-pass filter (HPF) — a powerful tool in both analog and digital electronics. Whether you’re working on audio systems, communication devices, or sensor circuits, understanding high-pass filters is essential.

In this guide, we’ll explore:

• what is high pass filter
• How it works
• Its types and real-world applications
• Circuit design with formulas
• FAQs to clear your doubts

Let’s dive in!

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What is a High-Pass Filter?

A high-pass filter is a circuit that allows signals with a frequency higher than a certain cutoff frequency to pass through, while attenuating lower-frequency signals. It essentially blocks “low” and lets “high” go.

High pass filter frequency response

In terms of frequency response:

• Frequencies above the cutoff: Pass through with little or no attenuation.
• Frequencies below the cutoff: Are attenuated (weakened) gradually or sharply.

Cutoff Frequency (fc)

The cutoff frequency is the point where the output signal drops to 70.7% (or -3 dB) of the input. This is the boundary between the “pass” and “attenuation” zones.

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High pass filter working principle 

Let’s start with a basic passive RC high-pass filter. It includes:

• A capacitor (C) in series with the input
• A resistor (R) connected to the ground after the capacitor

Basic RC High-Pass Filter Circuit:

High pass filter formula

 Formula for Cutoff Frequency:

 

$$f_c = \frac{1}{2\pi RC}$$

Where:

• f_c = cutoff frequency (Hz)
• R = resistance (ohms)
• C = capacitance (farads)

The capacitor blocks low frequencies by acting as an open circuit at low f, and allows high frequencies by acting as a short at high f.

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 Applications of High-Pass Filters

High-pass filters are used in almost every electronics domain. Here are some key applications:

1. Audio Systems

• Tone control- To remove low-frequency signals or remove hum or noise (e.g., < 60 Hz).
• In tweeters (speakers that handle high frequencies).

2. Communication Systems

• For modulation and demodulation.
• To eliminate DC offsets or drift.

3. Power Supplies

• To filter out ripple or unwanted low-frequency components.

4. Sensor Circuits

• In biomedical sensors (like ECGs) to remove baseline wander.

5. Digital Signal Processing (DSP)

• As software filters in image and sound processing.

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Types of High-Pass Filters

High-pass filters can be broadly categorized into analog and digital, and further into passive or active.

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1. Passive High-Pass Filter

It uses only passive components: resistors, capacitors, and/or inductors.

Advantages:

• Simple and cost-effective
• No power supply needed

Disadvantages:

• Cannot amplify signals
• Limited control over filter characteristics

Example: RC High-Pass Filter

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2. Active High-Pass Filter

Includes active components like operational amplifiers (Op-Amps) in addition to R and C.

Advantages:

• Can amplify signals
• Better performance at low frequencies
• Higher input impedance and lower output impedance

Disadvantages:

• Requires power supply
• Slightly complex

Example:
First-order Active HPF using Op-Amp.

3. First-Order and Second-Order High-Pass Filters

Filters are also categorized by their order, which affects the steepness of the cutoff.

A high-pass filter allows high-frequency signals to pass while attenuating low-frequency signals. The order of a high-pass filter refers to the steepness of its frequency response or roll-off rate after the cutoff frequency. Here’s the difference between first-order and second-order high-pass filters:

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First-Order High-Pass Filter

Key Features:

• Contains one reactive component (a capacitor or inductor).
• Roll-off rate: -20 dB/decade (or -6 dB/octave).
• Simple circuit design, typically RC (Resistor-Capacitor) or RL (Resistor-Inductor).

 Formula (RC Circuit)

Cutoff Frequency (fc):

$$f_c = \frac{1}{2\pi RC}$$

 

Circuit Diagram:

• Input → Capacitor → Resistor → Ground → Output taken across the resistor.

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Second-Order High-Pass Filter

Key Features:

• Contains two reactive components (like two capacitors or an op-amp + RC pair).
• Roll-off rate: -40 dB/decade (or -12 dB/octave).
• Sharper and more selective cutoff response than first-order.

Transfer Function:

$$H(s) = \frac{s^2}{s^2 + \frac{\omega_c}{Q}s + \omega_c^2}$$

 

Where:

• 
  $\omega_c = 2\pi f_c$ 
• 
  $\mathrm{<span\; style="font-size:\; 16px;">Q </span>}$ 

  $\mathrm{<span\; style="font-size:\; 16px;">=<span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;">\; Quality\; factor</span></span>}$ 

• Often implemented using active filters (op-amps) for better gain and stability.
• May use Sallen-Key topology for second-order active HPFs.

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Comparison Table

• Use first-order for basic, low-cost filtering.
• Use second-order when you need a steeper cutoff and better performance, especially in audio, instrumentation, or communication systems.

Let me know if you’d like circuit diagrams for both or a comparison graph!

• First-order: Attenuates at -20 dB/decade after cutoff.
• Second-order: Attenuates at -40 dB/decade (steeper).

Second-order filters use two capacitors and two resistors (or inductors), and can be designed using the Sallen-Key topology.

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Active First-Order High-Pass Filter:

Using a non-inverting Op-Amp configuration.

$$f_c=\frac{1}{2\pi R\mathrm{C<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"><span\; style="color:\; \#000000;"></span></span>}}$$

Gain is given by:

$$\text{Gain}=1+\frac{R_f}{R_{\mathrm{1<span\; class="vlist"\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"><span\; class="msupsub"\; style="color:\; \#000000;"><span\; class="vlist-s"></span></span></span>}}}$$

Where:

• R_f = feedback resistor
• R₁ =from inverting input to ground

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Second-Order Active High-Pass Filter (Sallen-Key)

The Sallen-Key topology is commonly used for precision filtering.

$$f_c = \frac{1}{2\pi \sqrt{R_1 R_2 C_1 C_2}}$$

​

$$Q = \frac{\sqrt{R_1 R_2 C_1 C_2}}{(R_1 + R_2)C_2}$$

​​Where

Q is the quality factor that determines the sharpness of the filter.

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Graph: Frequency Response Curve

A frequency response graph typically shows:

• X-axis: Frequency (log scale)
• Y-axis: Gain (dB)

At _fc gain drops to -3 dB.
Above _fc, gain stabilizes.
Below fc, gain rolls off.

High pass filter design

 Passive RC High-Pass Filter:

As explained earlier:

$$f_c=\frac{1}{2\pi R\mathrm{C<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"><span\; style="color:\; \#000000;"></span></span>}}$$

Example:

Suppose we want

$f_c = 1\, \text{kHz}$

  and we use

$C = 0.1\,\mu F$

Then,

$$R=\frac{1}{2\pi \times 1000\times 0.1\times {10}^{-6}}=1.59k\mathrm{\Omega }$$

 

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High-Pass Filter Design Tips

• Select accurate components: Tolerance matters near cutoff frequency.
• Use Op-Amp with good bandwidth for active designs.
• Simulate before building using tools like LTSpice or Falstad.
• Consider loading effects when connecting to other stages.

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Digital High-Pass Filters

In digital systems, high-pass filtering is done using digital signal processing (DSP) techniques.

Common Types:

• Finite Impulse Response (FIR) filters
• Infinite Impulse Response (IIR) filters

They use mathematical algorithms instead of physical components.

A simple digital HPF formula:

$$y[n]=a\cdot (y[n-1]+x[n]-x[n-1])$$

Where:

• x[n]= input signal
• $\mathrm{<span\; style="color:\; \#000000;"><span\; style="font-size:\; 16px;\; font-family:\; georgia,\; palatino,\; serif;"><em>y</em>[<em>n</em>]output\; signal</span></span>}$
• a= filter coefficient (0 < a < 1)

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Real-World Examples

• Smartphones: Remove background hum from voice.
• Guitar pedals: Enhance treble in audio signal.
• Medical devices: Eliminate slow-changing offsets in ECG signals.
• Wi-Fi modems: Filter out noise from nearby electrical equipment.

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Frequently Asked Questions (FAQs)

1. What is the main difference between low-pass and high-pass filters?

A low-pass filter passes low frequencies and blocks high ones. A high-pass filter does the opposite.

2. Can I build a high-pass filter using inductors?

Yes! An LC high-pass filter uses an inductor and capacitor instead of a resistor.

3. What happens at the cutoff frequency?

The output signal’s power drops to 50% (or voltage drops to 70.7%) of the input. This is the -3 dB point.

4. Is it better to use active or passive HPF?

It depends. Use passive for simplicity and low cost, active when you need amplification and better performance.

5. Can a high-pass filter remove DC?

Yes. A high-pass filter with a very low cutoff frequency can effectively block DC signals (0 Hz).

6. How does a digital high-pass filter differ from an analog one?

Digital filters use software and mathematical operations. Analog filters use physical components like resistors and capacitors.

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 Conclusion

A high-pass filter is a powerful and versatile circuit used in nearly every electronic system. From removing unwanted noise in audio systems to preparing signals in communication equipment, HPFs play a vital role in modern electronics.

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