RF signals are notoriously touchy. If you’re designing a military radar system, for example, a slight drift in a capacitor's value can shift the frequency just enough to cause interference or miss an incoming target. That’s why designing filters (in this case, high pass filters) requires careful attention to every detail.
One of the most critical aspects of any high pass filter design is the cutoff frequency, defined as the threshold where low-frequency signals are blocked and higher frequencies begin to pass. RF engineers need this to make sure their circuits pass only the desired signals while rejecting unwanted noise or interference.
We put this guide together to give RF engineers a trusted and no-nonsense method for calculating and adjusting LC high pass filter cutoff frequencies. Use it as a reference to meet your project’s specifications and avoid costly rework.
The cutoff frequency (fc) of an LC high pass filter is the point where higher frequency signals begin to pass through easily, while lower frequencies are blocked. In a common first-order LC high-pass filter, the capacitor (C) is placed in line with the signal, and the inductor (L) is connected to ground.
High Pass Filter Cutoff Frequency
Below the cutoff frequency, the capacitor resists the signal so it has a higher impedance compared to the inductor/coil. This shunts the signal to ground since the inductor has low impedance which allows signal to pass through easily so most of the signal is diverted to ground instead of continuing through the circuit.
Meanwhile, above the cutoff frequency, the inductor starts to resist the signal more (high impedance), while the capacitor resists it less (low impedance). This shift allows higher frequencies to pass through with minimal loss.
Engineers calculate the -3dB cutoff frequency for an ideal first-order LC high pass filter using the formula:
Where:
This formula determines the specific frequency at which the output power is half (or the voltage amplitude is approximately 70.7%) of the input power.
RF engineers must strategically select the values of L and C to precisely define this cutoff frequency and customize the filter's passband and stopband characteristics for specific application requirements.
It’s important to note that the filter's roll-off rate above the cutoff frequency is theoretically steeper compared to a simple RC or RL high pass filter, which improves its selectivity. Real-world component parasitics and loading effects can influence the actual frequency response.
It's no secret to an RF engineer how adjusting inductance and capacitance dictates a high-pass filter's cutoff frequency. Accurate selection of L and C values enables precise control over the filter's behavior and performance.
When you increase L, the inductive reactance (XL=2πfL) becomes high at a lower frequency. This means the inductor's impedance to ground becomes high sooner (at a lower frequency). Because the inductor is connected to ground, a higher impedance to ground means less shunting of the signal to ground. Therefore, the filter starts allowing signals to pass through earlier (at a lower frequency), thus lowering the cutoff frequency.
A higher capacitance also lowers the cutoff frequency. With more charge storage capacity, the capacitor better attenuates low-frequency signals, which reduces the cutoff frequency.
When either inductance or capacitance is reduced, the cutoff frequency increases. Reducing L and C values is particularly beneficial in RF applications requiring a higher cutoff frequency.
The physical size of inductors (L) and capacitors (C) typically corresponds to their electrical values. Higher inductance or capacitance often means larger components. Designers must carefully balance precise filtering requirements with the space and weight constraints of the overall system.
Changing the values of L or C to set the desired cutoff frequency affects the filter’s impedance and phase response, but has less impact on its steepness (roll-off) than increasing the number of filter sections or the filter order.
Since sensitive radar systems need a sharp roll-off to separate the signal from noise, RF engineers balance L and C values with size, filter order and performance requirements to achieve the best results.
Maintaining a stable and predictable frequency response despite temperature changes and aging requires high-precision LC components. To achieve this, RF engineers select components with low temperature coefficients and high Q-factors, which prevent cutoff frequency drift and maintain consistent long-term operation at the required frequencies.
RF engineers can use simulation tools to model the LC filter’s frequency response and make adjustments to L and C values based on performance benchmarks. Simulations allow engineers to visualize how component variations affect the filter’s cutoff frequency and overall response.
The unavoidable presence of unwanted inductance and capacitance in components, circuit board wiring, and even the filter’s physical enclosure can alter the actual cutoff frequency. For example, in a radar system, the metal casing of the filter might introduce stray capacitance, slightly shifting the filter’s response and causing it to pass unwanted frequencies.
RF engineers must consider these unintended "parasitics" when designing the filter and might add small adjustable components, like trimmer capacitors or inductors, to fine-tune the filter and counteract these effects.
High-power systems within the aerospace and defense (A&D) industry are particularly vulnerable to electromagnetic interference (EMI), which can introduce additional parasitic effects. Shielding and careful layout design help minimize these unwanted influences and preserve high filter performance.
Engineers often select custom components to satisfy the precise demands of an A&D mission. You can achieve your desired cutoff frequency while keeping the size to a minimum by using components like custom-wound inductors that provide higher inductance in a compact form, or precision ceramic capacitors with very low loss.
Mission-critical applications need temperature compensation to counteract the effects of temperature changes on electronic circuits and systems. This helps prevent cutoff frequency shifts caused by temperature swings. One way to maintain performance across a wide temperature range is to use a capacitor with high thermal stability or an inductor with magnetic compensation.
After simulating, engineers test the filter in real situations to check if it works as planned. They measure how the filter actually responds to different frequencies and then make small changes to its parts (L and C), often with adjustable pieces, to get the best performance. For military and space uses, these tests guarantee the filter works strongly and reliably in high altitudes or places with strong electrical interference.
Understanding the LC high pass filter cutoff frequency formula is important for RF engineers to design filters that meet signal requirements. But for actual applications, especially in military and aerospace, success depends on more than just calculations. Whether you're building a radar subsystem or a high-frequency communications filter, knowing how to apply this formula maintains precise cutoff frequencies and preserves signal integrity under operating conditions.
Building filters that work reliably in tough environments takes experience and careful engineering.
Q Microwave provides both off-the-shelf and custom RF filters and subsystems to support the complex requirements of modern defense and aerospace platforms. Every design is engineered with care to make sure it meets performance standards and withstand demanding environmental conditions. Contact Q Microwave to discuss how we can help you design high-quality high pass filters for your project.