Filter S-Parameters Explained: S21, S11, Return Loss and VSWR

S-parameters describe how a filter reflects and transmits RF energy at each of its ports over frequency, and they are the standard data format for characterising RF and microwave filters. A single S-parameter file contains the insertion loss, return loss, VSWR, rejection and group delay of a filter, measured under defined reference impedance conditions. This article explains what the four S-parameters of a two-port filter mean, how the common filter specifications are calculated from them, how a Touchstone file is structured, and how to analyse a measured file with a free Python tool, using a 9.5 GHz surface-mount bandpass filter as the example. It is written for RF design engineers and for component engineers who compare filters from datasheets and S-parameter data.

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Key Takeaways

Filter S-parameters relate the waves leaving each port to the waves arriving at each port; for a two-port filter there are four complex, frequency-dependent values: S₁₁, S₂₁, S₁₂ and S₂₂.
Insertion loss is −20 log₁₀|S₂₁| and return loss is −20 log₁₀|S₁₁|, both valid for the reference impedance of the data, usually 50 Ω.
For a passive filter, |S₁₁|² + |S₂₁|² ≤ 1; the difference is the power dissipated in the filter. In the example, 22 % of the incident power at 9.5 GHz is dissipated and only 1.9 % is reflected.
The phase of S₂₁ gives the group delay, which matters for modulated signals and radar pulses.
Plotting the full frequency range of an S-parameter file reveals effects that a passband plot hides, such as the spurious passband of the example filter above 23 GHz.
S-parameter files can be loaded directly into circuit simulators or analysed with open-source tools such as scikit-rf.

What S-Parameters Are

At high frequencies, voltages and currents vary along the connections, and broadband open and short circuits needed for Z-, Y- or H-parameters are difficult to realise. S-parameters therefore use travelling waves terminated in a defined reference impedance instead of total voltages and currents [1]. They are measured with a vector network analyser (VNA) and are complex quantities that depend on frequency [2].

Incident and outgoing waves

At each port i, the incident wave a_i and the outgoing wave b_i are defined from the forward and reverse voltage waves V_i⁺ and V_i⁻ and the reference impedance Z₀:

a_i = \frac{V_i^{+}}{\sqrt{Z_0}}, \qquad b_i = \frac{V_i^{-}}{\sqrt{Z_0}} \tag{1}

With this normalisation, |a_i|² and |b_i|² are proportional to the power arriving at and leaving port i. For a two-port network, such as a filter, the outgoing waves are linear combinations of the incident waves:

b_1 = S_{11}\,a_1 + S_{12}\,a_2, \qquad b_2 = S_{21}\,a_1 + S_{22}\,a_2 \tag{2}

Each parameter is measured with the other port terminated in Z₀, so that no wave returns into it. For example, S₁₁ and S₂₁ are measured with a₂ = 0 [2]:

S_{11} = \left.\frac{b_1}{a_1}\right|_{a_2 = 0}, \qquad S_{21} = \left.\frac{b_2}{a_1}\right|_{a_2 = 0} \tag{3}

Two-port network block diagram with incident waves a1 and a2, outgoing waves b1 and b2, and the S-parameter matrix S11, S12, S21, S22 — Figure 1. Two-port S-parameter matrix: a₁ and a₂ are the waves incident on ports 1 and 2, b₁ and b₂ are the outgoing waves.

The four S-parameters of a filter

Figure 1 shows the meaning of the four parameters. S₁₁ and S₂₂ are reflection coefficients, S₂₁ and S₁₂ are transmission coefficients [3]. For a passive filter, the transmission coefficients are always smaller than one, so the terms forward and reverse transmission describe them better than forward and reverse gain.

Parameter	Meaning	Filter specification	Ideal passband value	Ideal stopband value
S₁₁	Input reflection coefficient Γ_in	Input return loss, VSWR	\|S₁₁\| → 0 (large negative dB)	\|S₁₁\| → 1 (0 dB)
S₂₁	Forward transmission coefficient	Insertion loss, rejection, group delay	\|S₂₁\| → 1 (0 dB)	\|S₂₁\| → 0 (large negative dB)
S₁₂	Reverse transmission coefficient	Equal to S₂₁ for passive reciprocal filters	As S₂₁	As S₂₁
S₂₂	Output reflection coefficient Γ_out	Output return loss, VSWR	\|S₂₂\| → 0	\|S₂₂\| → 1

Table 1. Meaning of the four S-parameters of a two-port filter.

Passive filters made of capacitors, inductors, resonators and transmission lines without ferrites or active parts are reciprocal, so S₁₂ = S₂₁. A symmetrical filter also has S₁₁ = S₂₂. In measured data, small differences come from the test fixture and measurement uncertainty; in the example below, |S₂₁| and |S₁₂| differ by less than 0.15 dB across the passband.

Filter Specifications from S-Parameters

The common filter specifications are calculated directly from the magnitude and phase of the S-parameters [3], [4]. The equations below replace the original equation image.

Insertion loss and rejection

When source and load have the same impedance as the reference impedance of the data, the insertion loss is:

IL = -20\log_{10}\left|S_{21}\right| \ \mathrm{dB} \tag{4}

In the passband, IL is the loss of the wanted signal. In the stopband, the same quantity is called rejection or attenuation and is often given in dBc relative to the passband insertion loss [4]. How steeply the response moves from passband to stopband is described by the filter shape factor and selectivity.

Return loss and VSWR

The reflection coefficient at port 1 is Γ = S₁₁. Return loss expresses the reflected power in decibels and uses the magnitude of Γ:

RL = -20\log_{10}\left|\Gamma\right| = -20\log_{10}\left|S_{11}\right| \ \mathrm{dB} \tag{5}

The voltage standing wave ratio (VSWR) describes the same match as a ratio of maximum to minimum voltage on the line:

\mathrm{VSWR} = \frac{1 + \left|\Gamma\right|}{1 – \left|\Gamma\right|} \tag{6}

Return loss is a positive number for a passive port, while S₁₁ in decibels is negative; a return loss of 14 dB corresponds to S₁₁ = −14 dB. The output match is calculated in the same way from S₂₂.

Power balance and mismatch loss

For a passive two-port driven at port 1 and terminated in Z₀, the incident power is reflected, transmitted or dissipated. With P_diss the power dissipated in the filter and P_inc the incident power:

\left|S_{11}\right|^2 + \left|S_{21}\right|^2 = 1 – \frac{P_\mathrm{diss}}{P_\mathrm{inc}} \le 1 \tag{7}

Part of the insertion loss is caused by reflection rather than dissipation. This mismatch loss follows from S₁₁:

ML = -10\log_{10}\left(1 – \left|S_{11}\right|^2\right) \ \mathrm{dB} \tag{8}

Table 2 converts typical return loss values into reflection coefficient, VSWR, reflected power and mismatch loss.

Return loss	\|Γ\|	VSWR	Reflected power	Mismatch loss
6 dB	0.501	3.01	25.1 %	1.26 dB
10 dB	0.316	1.92	10.0 %	0.46 dB
14 dB	0.200	1.50	4.0 %	0.18 dB
20 dB	0.100	1.22	1.0 %	0.04 dB
30 dB	0.032	1.07	0.1 %	0.004 dB

Table 2. Return loss, reflection coefficient, VSWR, reflected power and mismatch loss calculated with Eq. (5), Eq. (6) and Eq. (8).

A return loss better than about 14 dB adds less than 0.2 dB of mismatch loss. In a well-matched filter, most of the passband insertion loss is therefore dissipation in conductors, dielectrics and resonators.

Group delay

The phase φ₂₁ of S₂₁ gives the group delay τ_g, the time a narrow-band signal envelope needs to pass through the filter:

\tau_g = -\frac{d\varphi_{21}}{d\omega} \tag{9}

Group delay is measured in seconds and is the derivative of the transmission phase with respect to angular frequency ω [4]. Its variation across the passband distorts modulated signals and short pulses, which is important in communication and radar applications. Group delay usually rises towards the band edges of a bandpass filter.

The Touchstone File Format

S-parameter data are exchanged as Touchstone files, a format specified by the IBIS Open Forum; version 2.1 was ratified in January 2024 [5]. Filenames traditionally use the extension .snp, where n is the number of ports, for example .s2p for a filter; the extension .ts is suggested for all versions.

Lines starting with ! are comments, which often record the instrument and the calibration or de-embedding state.
The option line, for example # MHz S DB R 50, gives the frequency unit (Hz, kHz, MHz or GHz), the parameter type (S, Y, Z, H or G), the data format (DB for dB and angle, MA for magnitude and angle, RI for real and imaginary) and the reference resistance.
Each data line of a two-port file contains the frequency followed by the four parameters. Version 1 files use the fixed order N₁₁, N₂₁, N₁₂, N₂₂; version 2 files declare the order with the keyword [Two-Port Data Order].
Version 2.0 and 2.1 add keywords such as [Version], [Number of Ports], [Reference] for different reference impedances per port, and [Mixed-Mode Order] for mixed-mode data.

The measured files of the example filter start with the option line # MHz S dB R 50: frequency in MHz, S-parameters in dB and degrees, 50 Ω reference [6]. Before using a file, check whether it contains the response of the bare component or includes the test board and connectors, because fixture loss and electrical length change both magnitude and phase.

Example: Plotting Filter S-Parameters with scikit-rf

The example uses the measured S-parameters of the Knowles DLI B095MB1S, a 9.5 GHz surface-mount bandpass filter with a passband of 8.9 to 10.0 GHz and a size of 10.16 × 3.80 × 2.61 mm [6]. Knowles, an EPCI member, publishes S-parameter data for its catalogue bandpass filters on the product pages [7]. The analysis uses scikit-rf, a free open-source Python package for RF and microwave engineering that can be run interactively in a Jupyter notebook [8].

Loading the file

The file was stored in a folder called xband2 and renamed B095MB1S.s2p. The following code loads it as a Network object and prints its summary [3]:

import skrf as rf import numpy as np ntwk = rf.Network('xband2/B095MB1S.s2p') print(ntwk) Result: 2-Port Network: 'B095MB1S', 2000.0-30000.0 MHz, 1601 pts, z0=[50.+0.j 50.+0.j]

The summary gives the frequency range, the number of points and the reference impedance of each port. A forward slash in the path works on Windows, Linux and macOS.

Plotting the S-parameters

The method plot_s_db plots the log magnitude in decibels. Without arguments it plots all four parameters; the indices m and n select a single parameter, counted from zero, so m = 1, n = 0 selects S₂₁ [8].

ntwk.plot_s_db() # all four S-parameters ntwk.plot_s_db(m=1, n=0) # S21 only

Figure 2 shows all four parameters in one plot, and Figure 3 shows each parameter individually.

Measured S11, S12, S21 and S22 magnitude in dB of the B095MB1S 9.5 GHz bandpass filter from 8 to 12 GHz plotted in one chart — Figure 2. All four measured S-parameters of the B095MB1S filter in one plot; source: Knowles Precision Devices.

Four separate plots of S11 input port reflection, S12 reverse transmission, S21 forward transmission and S22 output port reflection of the B095MB1S bandpass filter — Figure 3. Each S-parameter of the B095MB1S filter plotted individually; source: Knowles Precision Devices.

The plots show the typical shape of a bandpass filter. S₂₁ and S₁₂ lie on top of each other, as expected for a reciprocal filter. S₁₁ and S₂₂ show four distinct reflection minima across the passband, at about 8.97, 9.63, 10.02 and 10.35 GHz in sample 1. The ripple between the minima, which peaks near 9.33 GHz, sets the worst-case return loss.

Extracting the specifications

The same Network object gives the numbers that a datasheet specifies. The following lines select the 8.9 to 10.0 GHz passband and calculate the worst-case insertion loss, return loss, VSWR and group delay:

f = ntwk.f band = ntwk[(f >= 8.9e9) & (f <= 10e9)] print(-band.s_db[:, 1, 0].max()) # worst-case insertion loss, dB print(-band.s_db[:, 0, 0].min()) # worst-case input return loss, dB print(band.s_vswr[:, 0, 0].max()) # worst-case input VSWR print(np.real(band.s21.group_delay[:, 0, 0]).max()) # max. group delay, s

The zip file of the B095MB1S contains three measured samples. Table 3 compares their values with the datasheet [6].

Parameter	Sample 1	Sample 2	Sample 3	Datasheet
Insertion loss at 9.5 GHz	1.18 dB	1.12 dB	1.11 dB	–
Max. insertion loss, 8.9–10.0 GHz	1.60 dB	1.62 dB	1.61 dB	1.75 dB typ., 2.0 dB max.
Min. return loss S₁₁ / S₂₂, 8.9–10.0 GHz	12.9 / 12.6 dB	14.4 / 13.9 dB	13.3 / 13.0 dB	14.0 dB typ., 10.0 dB min.
Max. VSWR (input), 8.9–10.0 GHz	1.59	1.47	1.56	–
Min. rejection, 2–8 GHz	48.7 dB	49.7 dB	48.6 dB	45 dB typ., 40 dB min. (DC–8 GHz)
Min. rejection, 11.5–20 GHz	45.2 dB	44.9 dB	46.4 dB	45 dB typ., 40 dB min.
3 dB bandwidth	8.76–10.47 GHz	8.77–10.47 GHz	8.77–10.47 GHz	–
Group delay, 8.9–10.0 GHz	1.01–1.47 ns	1.01–1.48 ns	0.99–1.47 ns	–

Table 3. B095MB1S measured S-parameter data evaluated with scikit-rf, compared with the datasheet values.

All three samples meet the datasheet limits with margin. The power balance of Eq. (7) shows where the passband loss goes: at 9.5 GHz, sample 1 has |S₂₁|² = 0.762 and |S₁₁|² = 0.019, so 22 % of the incident power is dissipated in the filter. The mismatch loss from Eq. (8) is only 0.08 dB of the 1.18 dB insertion loss; the remaining 1.10 dB is dissipation.

Looking beyond the passband

The plots in Figures 2 and 3 cover 8 to 12 GHz, but the file contains data from 2 to 30 GHz. Plotting the full range shows that above 11.5 GHz the rejection stays above 40 dB up to about 23.5 GHz and then collapses: a spurious passband appears between about 25 and 30 GHz, with a minimum insertion loss of 1.2 to 1.6 dB in the three samples. Distributed filters built from transmission-line resonators repeat their response at higher frequencies. The datasheet specifies rejection only up to 20 GHz [6], so a system with signals or harmonics above 23 GHz needs an additional low-pass filter.

S-Parameters of Other Passive Components

S-parameters are not limited to RF filters. Manufacturers provide S-parameter files for capacitors, inductors, ferrite beads and EMI filters, and bypass capacitor S-parameter models are widely used in power integrity simulation.

Impedance from a two-port measurement

Low impedances, such as those of capacitors and power distribution networks, are measured with the 2-port shunt-through method. The component is connected between the signal line and ground at the junction of both VNA ports, and its impedance follows from S₂₁ [9]:

Z_\mathrm{DUT} = 25\ \Omega \cdot \frac{S_{21}}{1 – S_{21}} \tag{10}

The expression is exact for 50 Ω ports, and for impedances well below 5 Ω it simplifies to Z_DUT ≈ 25 Ω · S₂₁. The fixture should be shorter than about 1/20 of the wavelength at the highest measured frequency; a 25 mm (1 inch) connection limits accurate results to about 300 MHz [9].

Mixed-mode S-parameters

Components with four terminals, such as common mode chokes for differential lines, are described with four-port S-parameters converted into mixed-mode parameters. S_dd21 is the differential-mode transmission, which should stay close to 0 dB to preserve the wanted signal, and S_cc21 is the common-mode transmission, whose negative value is the common-mode insertion loss that suppresses noise [10]. Differential lines typically use a 100 Ω (sometimes 90 Ω) differential reference impedance instead of 50 Ω.

Practical Considerations

S-parameter data are only as useful as the conditions they were measured under. The following points determine whether a file represents the filter in the application.

Reference impedance: the equations for insertion loss and return loss apply to the reference impedance of the file. In a system with other impedances, use the full S-parameter set in a circuit simulator rather than the IL figure alone.
De-embedding: check whether the data are de-embedded to the component terminals or include the test board. The typical curves in the B095MB1S datasheet, for example, are de-embedded measurements on a connectorised test fixture with a 0.25 mm RO4350B board and 50 Ω coplanar waveguide traces, while the specifications are based on probed performance at room temperature [6].
Frequency range and resolution: the file should cover all frequencies present in the system, including harmonics and spurious responses. The 17.5 MHz step of the example file is fine enough for a 1.7 GHz wide passband but not for very narrow filters.
Temperature and power: S-parameter files are usually measured at room temperature and low signal level. The B095MB1S datasheet specifies an insertion loss variation of ±0.5 dB over temperature [6].
Sample variation: one file represents one sample. Compare several samples or the datasheet limits before setting system margins.
Linearity: S-parameters describe linear behaviour. Saturating ferrites or other nonlinear materials need measurements at the operating conditions.

Selection Checklist

Passband insertion loss: worst-case value across the band, not only the centre value.
Return loss or VSWR at both ports across the passband.
Rejection in all stopbands that matter for the system, including spurious passbands far above the passband.
Group delay and its variation for modulated or pulsed signals.
Reference impedance, de-embedding state, frequency range and step of the S-parameter file.
Temperature range, power handling and mounting conditions specified for the data.
Availability of S-parameter files for several samples or of a simulation model for system-level design.

Conclusion

S-parameters describe a filter completely as a linear two-port: S₁₁ and S₂₂ give the input and output match, S₂₁ gives insertion loss, rejection and group delay, and the power balance separates reflected from dissipated power. Insertion loss, return loss and VSWR follow from simple equations, provided the source and load correspond to the reference impedance of the data.

Open-source tools such as scikit-rf make it easy to load a Touchstone file, plot the parameters and extract worst-case values. Evaluating the full frequency range of the file, as in the example with its spurious passband above 23 GHz, and checking the measurement conditions are as important as reading the passband values.

FAQ

What are S-parameters of a filter?

S-parameters, or scattering parameters, describe how a filter reflects and transmits RF waves at each port over frequency. For a two-port filter there are four complex values: S11 and S22 are the input and output reflection coefficients, S21 and S12 are the forward and reverse transmission coefficients. They are measured with a vector network analyser with all ports terminated in a reference impedance, usually 50 ohms.

How is insertion loss calculated from S21?

Insertion loss is minus twenty times the base-10 logarithm of the magnitude of S21, expressed in decibels. An S21 of minus 1.2 dB therefore means an insertion loss of 1.2 dB. The calculation is valid when the source and load impedances equal the reference impedance of the S-parameter data, which is normally 50 ohms for RF filters.

What is the difference between return loss and S11?

S11 is the input reflection coefficient, a complex number whose magnitude in decibels is negative for a passive port. Return loss is minus twenty times the logarithm of the magnitude of S11 and is given as a positive number. A return loss of 14 dB therefore corresponds to an S11 of minus 14 dB, a reflection coefficient of 0.2 and a VSWR of 1.5.

How is VSWR calculated from S-parameters?

VSWR is calculated from the magnitude of the reflection coefficient, which equals the magnitude of S11 at the input or S22 at the output. VSWR equals one plus the magnitude divided by one minus the magnitude. A reflection coefficient of 0.1, which is 20 dB return loss, gives a VSWR of 1.22, and 0.316, which is 10 dB return loss, gives 1.92.

Why is S12 equal to S21 for a passive filter?

Passive filters built from capacitors, inductors, resonators and transmission lines are reciprocal networks, so the transmission from port 1 to port 2 equals the transmission from port 2 to port 1. In measured data the two values differ slightly because of fixture and measurement uncertainty. Components with ferrites in a magnetic bias field or active parts can be non-reciprocal.

Where does the insertion loss of a filter go?

Part of the incident power is reflected and part is dissipated in conductors, dielectrics and resonators. The sum of the squared magnitudes of S11 and S21 shows the share that is reflected and transmitted; the rest is dissipated. In the 9.5 GHz example filter, only 1.9 percent of the power is reflected, while 22 percent is dissipated, so the loss is mainly dissipative.

What is a Touchstone s2p file?

A Touchstone file is the standard text format for S-parameter data, specified by the IBIS Open Forum. The extension s2p stands for a two-port network. After comment lines, an option line defines the frequency unit, parameter type, data format and reference resistance, followed by data lines with the frequency and the four parameters. Circuit simulators and tools such as scikit-rf read the format directly.

Why should the full frequency range of an S-parameter file be checked?

Datasheet plots often show only the passband and nearby stopbands. Distributed filters can have spurious passbands at higher frequencies, where the rejection collapses. In the 9.5 GHz example, rejection stays above 40 dB up to 23.5 GHz but a spurious passband appears between about 25 and 30 GHz. Signals or harmonics in that range would pass the filter almost without attenuation.

How to Evaluate a Filter from Its S-Parameter File

Step-by-step procedure for evaluating the performance of an RF filter from its measured S-parameter file.

Obtain the S-parameter file
Download the Touchstone file of the filter from the manufacturer and note whether it contains de-embedded component data or includes a test fixture.
Check the file header
Read the comment lines and the option line to confirm the frequency unit, data format and reference impedance, usually 50 ohms.
Load the file
Load the file into a circuit simulator or into scikit-rf as a Network object and check the frequency range and number of points.
Plot all four parameters
Plot S11, S21, S12 and S22 in decibels over the full frequency range of the file to see the passband, stopbands and any spurious passbands.
Extract the specifications
Calculate worst-case insertion loss from S21, return loss and VSWR from S11 and S22, rejection in each stopband and group delay from the phase of S21.
Compare with the requirements
Compare the extracted values with the datasheet limits and the system requirements, including temperature variation and sample spread.
Simulate in the system
Use the full S-parameter set in a circuit simulation with the real source and load impedances when they differ from the reference impedance.

References

S-Parameter Design, Application Note 154 (5952-1087), Keysight Technologies.
Two-port Measurements and S-Parameters, University Engineering Lab Series, Lab 5, application note 5992-0249EN, Keysight Technologies, 2015.
P. Matthews, Filter Basics 11: What Are S-Parameters and What Can They Tell Us About a Filter?, Knowles Precision Devices, 2022.
P. Matthews, RF Filter Terminology and Specifications, Knowles Precision Devices blog, 2023.
Touchstone File Format Specification, Version 2.1, IBIS Open Forum, 2024.
9.5 GHz Surface Mount Bandpass Filter B095MB1S, datasheet, Knowles Precision Devices (DLI), June 2025; measured S-parameter data B095MB1S, Touchstone files 1–3.
Bandpass Filters – product overview and S-parameter data, Knowles Precision Devices (DLI).
scikit-rf – open-source Python package for RF and microwave engineering, and Network.plot_s_db documentation, scikit-rf project.
Ultra-Low Impedance Measurements Using 2-Port Measurements, application note 5989-5935EN, Keysight Technologies, 2014.
Noise Suppression in Differential Transmission, Guidelines for EMI Suppression, Section 2, Murata Manufacturing.
Knowles – EPCI premium supplier page, Passive Components Blog.

Article revised and technically reviewed in November 2026: converted the equation and code images into equations and text, corrected the return loss equation and the wave definitions in Figure 1, added the S-parameter definitions, power balance, mismatch loss, group delay, the Touchstone format, a scikit-rf analysis of the measured B095MB1S data with comparison to the datasheet and the spurious passband, impedance and mixed-mode S-parameters of other passive components, practical considerations, checklist, FAQ and How-to, and added referenced sources.

Source: Knowles Precision Devices