Basic Filter Circuits Explained: RC, RL and LC

Basic filter circuits use the frequency-dependent impedance of capacitors and inductors to pass wanted signals and attenuate unwanted frequencies. This article explains voltage dividers, RC low-pass and high-pass filters, RL substitutions, and LC networks for design and component engineers, with practical guidance on loading, component selection, and validation.

How to Measure Filter Performance: Insertion Loss, VNA Fixtures and CM/DM Separation

Passive Filter Technologies Compared: LC, Ferrite, Feedthrough, Ceramic, Cavity, Microstrip, SAW and BAW

Knowles A-Series RF Attenuators Target Compact 20 GHz Designs

The starting point is lumped-element signal and RF filtering using resistors, capacitors, and inductors. The same impedance principles also apply to power filters, but power-handling, magnetic saturation, thermal behavior, and interaction with the surrounding converter require additional analysis. The original circuit illustrations and explanatory sequence are adapted from the Knowles Precision Devices article on designing basic filter circuits.

Key Takeaways

A passive filter can be understood as a voltage divider whose impedances change with frequency.
An RC low-pass filter uses a series resistor and a shunt capacitor; an RC high-pass filter uses a series capacitor and a shunt resistor.
The familiar RC cutoff expression assumes an ideal source and negligible output loading. Real source and load impedances can change both gain and cutoff.
Filter order determines the asymptotic roll-off of an all-pole response. LC networks allow useful higher-order responses, but their damping and terminations must be considered.
Actual performance depends on component losses, tolerances, bias, self-resonance, and PCB layout, not only the nominal resistance, capacitance, and inductance.

Basic Filter Circuits Start with a Voltage Divider

A filter does not need to be treated as a completely new circuit concept. Start with the familiar resistive voltage divider, then replace one or both resistances with impedances that vary with frequency. A resistive voltage divider is a passive linear circuit whose output voltage, V_o, is a fraction of its input voltage, V_i. In Figure 1, R₁ is the series resistance between the input and output, and R₂ connects the output to the reference node. The output is measured across R₂.

Resistive voltage divider with series resistance R1 and shunt resistance R2. — Figure 1. A resistive voltage divider provides the starting point for understanding passive filters.

Ohm’s law relates voltage, current, and resistance. With negligible current drawn by the output load, both resistors carry the same current, so the output follows Eq. (1). Here V_i and V_o are voltages in V, and R₁ and R₂ are resistances in Ω.

V_o = V_i \frac{R_2}{R_1 + R_2} \tag{1}

Increasing R₁, or decreasing R₂, reduces the unloaded output voltage. If another circuit draws appreciable current from the output, its input impedance becomes part of the divider and the unloaded relationship no longer describes the complete circuit.

Swapping Resistors and Capacitors to Create RC Filters

Replacing a divider resistor with a capacitor makes the division ratio frequency-dependent. The position of the capacitor determines whether the circuit attenuates high frequencies or low frequencies. The following explanations assume ideal components, an ideal voltage source, and negligible output loading unless stated otherwise. [1]

The impedance of an ideal capacitor decreases in magnitude as frequency increases. Eq. (2) describes this capacitive impedance; it is not an equation for calculating capacitance.

Z_C = \frac{1}{j\omega C} \tag{2}

In Eq. (2), Z_C is capacitor impedance in Ω, C is capacitance in F, and ω is angular frequency in rad/s. Angular frequency is related to frequency f in Hz by ω = 2πf. The symbol j is the imaginary unit, with j² = −1; some references use i instead. The same j notation is used throughout this article. [1]

RC Low-Pass Filter

Replace R₂ in the divider with a capacitor. The resulting RC low-pass filter has a series resistance R and a shunt capacitance C, with the output taken across the capacitor, as illustrated in Figure 2.

At low frequencies, the capacitor presents a high impedance, so little current flows through the series resistor and the output approaches the input. At higher frequencies, the capacitor impedance falls, more current flows through the resistor, and the output voltage decreases. This is continuous attenuation, not an abrupt boundary between complete transmission and complete blocking. [1]

RC low-pass filter with a series resistor and a capacitor from the output to the reference node. — Figure 2. RC low-pass filter with a series resistor and a shunt capacitor.

RC low-pass frequency response showing decreasing output amplitude as frequency increases. — Figure 3. The output amplitude of an RC low-pass filter decreases as frequency increases.

Define the dimensionless voltage transfer function H_LP as V_o/V_i. For the ideal unloaded circuit, Eq. (3) describes its low-pass response. R is the series resistance in Ω and C is the shunt capacitance in F. [1]

H_{\mathrm{LP}}(j\omega) = \frac{V_o}{V_i} = \frac{1}{1+j\omega RC} \tag{3}

The capacitor provides a return path for AC current, but an ideal capacitor does not dissipate average power. It stores and returns energy; the resistance dissipates power. Consequently, describing the filter simply as sending unwanted energy into ground obscures how voltage division and the current return path actually work.

RC High-Pass Filter

Now replace R₁, rather than R₂, with a capacitor. The input reaches the output through the series capacitor, while a resistor connects the output to the reference node. The output is measured across that resistor, as shown in Figure 4.

At low frequencies, the series capacitor has a high impedance, limiting current and producing a small output voltage across the resistor. At higher frequencies, its impedance decreases and the output approaches the input. The capacitor blocks steady DC in the ideal model; the rejected low-frequency signal is not simply routed through the resistor into ground. [1]

RC high-pass filter with a series capacitor and a resistor from the output to the reference node. — Figure 4. RC high-pass filter with a series capacitor and a shunt resistor.

RC high-pass frequency response showing increasing output amplitude toward the passband value. — Figure 5. The output amplitude of an RC high-pass filter increases toward its passband value as frequency increases.

For the same ideal-source and unloaded-output assumptions, define the dimensionless high-pass transfer function H_HP as V_o/V_i. Its response is given by Eq. (4), where R is the shunt resistance and C is the series capacitance. [1]

H_{\mathrm{HP}}(j\omega) = \frac{V_o}{V_i} = \frac{j\omega RC}{1+j\omega RC} \tag{4}

Cutoff Frequency and Roll-Off

The ideal RC circuits in Eqs. (3) and (4) share the cutoff frequency f_c in Eq. (5). With R in Ω and C in F, f_c is in Hz. At this frequency, the output magnitude is approximately 0.707 of its passband value, corresponding to approximately −3 dB. [1]

f_c = \frac{1}{2\pi RC} \tag{5}

A first-order low-pass filter approaches a roll-off of −20 dB per decade above its cutoff. A first-order high-pass filter approaches a slope of +20 dB per decade as frequency increases through the low-frequency stopband. These are asymptotic slopes, not the exact slope at the corner. The corresponding phase shift also matters when filtering signals in a control or feedback path. [1]

Swapping Capacitors and Inductors to Create RL and LC Filters

An ideal inductor has the opposite impedance trend to an ideal capacitor: its impedance magnitude increases with frequency. Changing the reactive component therefore changes which frequencies are attenuated, provided its position and the output measurement remain clearly defined.

The ideal inductive impedance is given by Eq. (6). Here Z_L is inductor impedance in Ω and L is inductance in H; j and ω retain the definitions introduced for Eq. (2). This is an impedance relationship, not an equation for calculating inductance.

Z_L = j\omega L \tag{6}

The ideal trends in Eqs. (2) and (6) have limits in real components because of losses and parasitic capacitance or inductance. Check frequency-dependent component data rather than extending the ideal equations indefinitely. [2, 3, 4]

Changing the Filter Type with an RL Network

Start with the RC high-pass filter in Figure 4 and replace the series capacitor with an inductor. At low frequencies the ideal inductor presents little impedance, while at higher frequencies its impedance rises and reduces the output across the shunt resistor. The resulting RL network is a low-pass filter.

Alternatively, start with the RC low-pass filter in Figure 2 and replace the shunt capacitor with an inductor. At low frequencies the inductor holds the output close to the reference potential. At higher frequencies its impedance rises, allowing a larger output voltage. The resulting RL network is a high-pass filter. Figure 6 illustrates both substitutions.

Comparison of RC and RL circuits showing how replacing a capacitor with an inductor reverses the filter type. — Figure 6. Replacing a shunt capacitor with an inductor changes the illustrated low-pass network into a high-pass network; replacing a series capacitor with an inductor changes the illustrated high-pass network into a low-pass network.

Combining Capacitors and Inductors

Combining inductors and capacitors provides additional freedom to shape low-pass, high-pass, and band-pass responses, as illustrated in Figure 7. LC filters are particularly useful where a series resistance would create unacceptable loss, although actual inductors and capacitors still have losses. [2]

Comparison of LC filter configurations and their low-pass, high-pass, and band-pass responses. — Figure 7. Examples of LC filter configurations and their frequency responses.

The important distinction is filter order and response, not a blanket rule that RC filters have poor roll-off. A second-order all-pole low-pass response can approach −40 dB per decade in its high-frequency stopband, compared with −20 dB per decade for a first-order response. Higher-order RC implementations are also possible, but interaction between passive stages must be included. [1]

LC networks can resonate. Their source and load impedances, component losses, and any intentional damping determine whether the response is acceptably smooth or exhibits unwanted peaking. Selecting L and C alone does not establish a complete filter specification. Response families such as Butterworth, Bessel, Chebyshev, and elliptic offer different compromises between amplitude flatness, transition sharpness, ripple, and phase behavior. [1, 2]

Manipulating Impedance to Achieve the Desired Frequency Response

The voltage-divider viewpoint extends beyond individual resistors, capacitors, and inductors. Each arm can be an impedance network, allowing a more complex frequency response while retaining the same basic analysis approach.

In Figure 8, Z₁ represents the series impedance and Z₂ the shunt impedance. The output is taken across Z₂. A high-pass response can be obtained when the division ratio increases with frequency, for example when the series impedance decreases while the shunt impedance increases over the intended operating band.

Generalized voltage divider with series impedance Z1 and shunt impedance Z2. — Figure 8. Generalized voltage divider using a series impedance Z1 and a shunt impedance Z2.

The individual impedance trends are a useful starting point, but the complex ratio determines the actual response. Phase, resonance, and loading can prevent a network from behaving like a simple magnitude-only divider. Replacing individual components with RC or LC subnetworks therefore requires analysis of the complete connected circuit. [1, 2]

Include Source and Load Impedance

For a low-pass RC circuit, a resistive source impedance adds to the series resistance, while a resistive load appears in parallel with the capacitor. Both can alter the response, and the load can reduce the passband output. In the high-pass circuit, the load changes the effective shunt resistance and the source resistance also affects the division ratio. Eq. (5) must therefore not be used unchanged unless its assumptions apply. [1]

Likewise, connecting passive stages directly can load the preceding stage. Analyze the combined network, provide suitable impedance separation, or use a buffer where an active stage is acceptable. For RF filters, use the intended source and load terminations in both simulation and measurement; a response obtained under different terminations may not represent the installed circuit. [1, 2]

Design and Component Selection Checklist

Nominal component values establish a starting point, not a validated design. Compare electrical performance under the actual frequency, bias, temperature, source, and load conditions before selecting parts or approving substitutes. [2, 3, 4]

Define the passband, allowable loss or amplitude error, required stopband attenuation, and transition region. Include phase or waveform requirements when they affect the application.
Check resistance tolerance, power dissipation, and the consequences of source and load impedance. Do not substitute resistor values without checking the connected network.
For capacitors, compare tolerance, dielectric behavior, effective capacitance at the operating DC bias and temperature, equivalent series resistance, equivalent series inductance, and self-resonant frequency. Class 2 ceramic capacitance can change appreciably with applied voltage; nominal capacitance alone may be misleading. [3]
For inductors, compare inductance at the relevant frequency and bias, tolerance, DC resistance, quality factor, self-resonant frequency, and current ratings. Check how the manufacturer defines saturation and temperature-rise limits before comparing alternatives. [4]
Check LC peaking and transient behavior with the actual terminations. Component quality factor and circuit quality factor are related but are not interchangeable specifications. [1, 2]
Start with catalog components where they meet the requirements. Re-simulate using available values and realistic models. Consider a custom component or network when the electrical, mechanical, or environmental requirements cannot be met by standard parts, and agree the verification conditions with the supplier. [2, 4]
For power or SMPS applications, additionally verify inductor saturation, heating, capacitor current capability, and the filter’s interaction with the converter. The small-signal diagrams in this article are not a complete power-filter design procedure.
Confirm application-specific qualification and safety requirements separately. A nominal capacitance, inductance, or voltage rating does not by itself establish suitability for every installation.
Include PCB traces, pads, and current-return paths in high-frequency analysis. Keep relevant loops compact, use measurement-based component models where available, and validate a prototype using the intended source and load conditions. [2, 4]

Real capacitors stop following the ideal decreasing-impedance trend when parasitic inductance becomes significant, while inductor parasitic capacitance limits ideal inductive behavior. Check the component’s frequency-dependent data over the required passband and stopband rather than relying only on a single nominal value. The related explanation of capacitor losses, ESR, impedance, and quality factor develops these practical capacitor parameters. [2, 3, 4]

Conclusion

Basic passive filters are frequency-dependent voltage dividers. Moving a capacitor between the series and shunt positions produces RC high-pass or low-pass behavior, while substituting an inductor reverses the ideal frequency trend. Combining reactive elements allows more complex responses, but the result depends on filter order, damping, and termination as well as component values.

Use the ideal relationships to understand the circuit and choose initial values. Then include source and load impedances, realistic component behavior, and PCB parasitics, and verify the connected circuit before finalizing component selection.

FAQ

What is the difference between an RC low-pass and high-pass filter?

An RC low-pass filter uses a series resistor and a shunt capacitor, with the output across the capacitor. An RC high-pass filter uses a series capacitor and a shunt resistor, with the output across the resistor. The capacitor position changes whether high or low frequencies are attenuated.

What does the cutoff frequency of an RC filter mean?

For the ideal first-order RC circuits described here, the cutoff frequency is where output amplitude is approximately 0.707 of the passband value, or approximately −3 dB. It is not an abrupt blocking frequency. The familiar calculation assumes an ideal voltage source and negligible output loading; other impedances must be included when present.

Why does a passive filter change when it is connected to another circuit?

The receiving circuit presents an input impedance that becomes part of the filter, while the driving circuit contributes source impedance. These impedances can change passband gain, cutoff, and damping. Analyze or measure the complete connected network rather than assuming that an unloaded filter response remains unchanged after installation.

Is an LC filter always better than an RC filter?

No. The appropriate choice depends on loss, frequency response, size, loading, and application requirements. LC networks can provide useful higher-order responses without an intentional series resistor, but real components still have losses and the network can resonate. Filter order and damping matter more than a general RC versus LC ranking.

Which component specifications matter when selecting filter parts?

Compare tolerances and behavior at the actual frequency, bias, and temperature. For capacitors, review effective capacitance, losses, parasitic inductance, and self-resonance. For inductors, review inductance, resistance, quality factor, self-resonance, and current-rating definitions. Also confirm the required qualification, physical layout, source and load conditions, and prototype performance before approving substitutes.

How to Select and Validate a Basic Passive Filter

Use this procedure to move from an ideal passive-filter concept to a connected and verified circuit.

Define the required response
Identify the wanted frequency range, unwanted frequencies, allowable passband loss, and required attenuation. Record the actual source and load impedances and any phase or waveform constraints.
Choose the circuit and initial values
Select an RC, RL, or LC network appropriate to the response and loss requirements. Calculate initial values using the relevant assumptions, then include source and load impedances in the connected circuit.
Check real components and layout
Select available parts and evaluate tolerances, bias, temperature, losses, and self-resonance. Check current and thermal limits where applicable, include important PCB parasitics, and confirm application-specific qualification and safety requirements.
Measure the connected prototype
Build the filter and measure its response with the intended source and load conditions. Compare passband loss, cutoff, stopband attenuation, and any peaking with the requirements, then revise the design and validate proposed substitutes.

References

The following documents support the transfer-function, practical-component, and implementation guidance above.

Hank Zumbahlen, Phase Relations in Active Filters, Analog Devices, Analog Dialogue, 2007.
Coilcraft, Passive LC Filter Design and Analysis, Coilcraft application note, publication year not stated.
Murata Manufacturing, Basics of Ceramic Capacitors, Murata Manufacturing, publication year not stated.
Murata Power Solutions, Inductors: Application Notes, Murata Power Solutions, revision A03, publication year not stated.

Latest technical review and revision: 5 November 2026. Updated impedance terminology, converted the original equation images to mathematical notation, added RC response equations and loading assumptions, and expanded practical selection guidance.

Source: Knowles Precision Devices