resonantFrequency

R2026b

Calculate and plot resonant frequency of antenna

Since R2024a

Syntax

resonantFrequency(object,frequency)

resonantFrequency(object,frequency,Method="Sparameters")

resonantFrequency(___,Name=Value)

fRES = resonantFrequency(object,frequency)

fRES = resonantFrequency(object,frequency,Name=Value)

[fRES,zRES,Z,typRES] = resonantFrequency(object,frequency)

[fRES,zRES,Z,typRES] = resonantFrequency(object,frequency,Name=Value)

[fRES,sRES,S] = resonantFrequency(object,frequency,Method="Sparameters")

[fRES,sRES,S] = resonantFrequency(object,frequency,Method="Sparameters",Name=Value)

[___,sweepobj] = resonantFrequency(___,SweepOption=Value)

Description

resonantFrequency(object,frequency) marks the resonant frequencies on the impedance plot of the specified antenna or array in the specified frequency range. If the function detects no resonant frequency in the specified frequency range, it plots the impedance of the antenna or array without any marked points.

resonantFrequency(object,frequency,Method="Sparameters") marks the resonant frequencies on the S₁₁ plot. If the function detects no resonant frequency in the specified range, it plots the S₁₁ of the antenna or array without any marked points.

resonantFrequency(___,Name=Value) specifies additional options using one or more name-value arguments, in addition to any of the input argument combinations from the previous syntaxes. For example, resonantFrequency(dipole,60e6:1e6:80e6,Threshold=15) marks the resonant frequencies of the dipole antenna on the impedance plot in the 60 MHz to 80 MHz range with a threshold of 15 ohms.

fRES = resonantFrequency(object,frequency) returns the resonant frequencies fRES of the specified antenna or array in the specified frequency range. fRES is empty if the function detects no resonant frequency in the specified frequency range, and is a vector if the function detects more than one resonant frequency.

fRES = resonantFrequency(object,frequency,Name=Value) specifies additional options using one or more name-value arguments. For example, fRES = resonantFrequency(dipole,60e6:1e6:80e6,Mthod="Sparameters",Threshold=-10) marks the resonant frequencies on the S₁₁ plot of the dipole antenna in the 60 MHz to 80 MHz range with an S₁₁ threshold of -10 dB.

[fRES,zRES,Z,typRES] = resonantFrequency(object,frequency) also returns the impedances zRES and the resonance types typRES (series or parallel) corresponding to the resonant frequencies fRES, and the impedance values Z across the specified frequency range. zRES is a vector and typRES is a string array if the function detects more than one resonant frequency.

[fRES,zRES,Z,typRES] = resonantFrequency(object,frequency,Name=Value) specifies additional options using one or more name-value arguments.

[fRES,sRES,S] = resonantFrequency(object,frequency,Method="Sparameters") returns the resonant frequencies fRES, the corresponding S₁₁ values sRES, and the S₁₁ values S across the specified frequency range. sRES is a vector if the function detects more than one resonant frequency.

[fRES,sRES,S] = resonantFrequency(object,frequency,Method="Sparameters",Name=Value) specifies additional options using one or more name-value arguments.

[___,sweepobj] = resonantFrequency(___,SweepOption=Value) uses the specified frequency sweep interpolation method to calculate the resonant frequencies, and additionally returns the interpolation method type and rational fit parameters stored in a frequency sweep object sweepobj. You can use this syntax with any of the output argument combinations from the previous syntaxes.

Examples

Calculate and Plot Resonant Frequency of Dipole Antenna

This example shows how to calculate and plot the resonant frequency of a dipole antenna using Impedance method and S-parameters method.

Calculate and Plot Resonant Frequency using Impedance Method

Create a dipole antenna operating at 75 MHz. Calculate and plot the resonant frequency of a dipole over a frequency span of 50 MHz - 100 MHz.

h = design(dipole,75e6);
resonantFrequency(h,50e6:1e6:100e6);

Calculate and Plot Resonant Frequency using S-parameters Method

Calculate and plot the resonant frequency of the same dipole, using S-parameters method, over the same frequency span.

resonantFrequency(h,50e6:1e6:100e6,Method="Sparameters");

Input Arguments

object — Antenna or array to calculate resonant frequency

antenna object | pcbStack object | customAntenna object | customAntennaMesh object | customAntennaGeometry object | infiniteArray object

Antenna or array to calculate resonant frequency, specified as one of the following options:

• Antenna object from the antenna catalog.

• pcbStack object.

• customAntenna object.

• customAntennaMesh object.

• customAntennaGeometry object.

• infiniteArray object.

Example: dipole

frequency — Frequency range to calculate resonant frequency

positive vector

Frequency range to calculate the resonant frequency, specified as a positive vector in Hertz.

Example: [50e6:5e6:80e6]

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: Method="Sparameters"

UseParallel — Option to enable parallel pool

false (default) | true | 0 | 1

Option to enable parallel pool, specified as a logical value. The default value is false. Set this option to true or 1 to enable the parallel pool. Use parallel pool to speed up the resonant frequency calculations at multiple frequencies for computationally large antennas and arrays. To use this feature, you need a license to the Parallel Computing Toolbox™.

Example: UseParallel=true

Data Types: logical

Method — Method to use for resonant frequency calculation

"Impedance" (default) | "Sparameters"

Method to use for resonant frequency calculation, specified as either "Impedance" or "Sparameters". The default method is "Impedance". When the method is specified as "Impedance", zero-crossings of the reactance are used to find the resonant frequency, and zRES and Z are the outputs. When the method is specified as "Sparameters", the negative peaks of S₁₁ are used to find the resonant frequency. The output typRES (whether the impedance is series or parallel) is supported only when the method is "Impedance".

Example: "Sparameters"

Data Types: string

SweepOption — Sweep interpolation method

"direct" (default) | "interp" | "interpWithGrad" | frequencySweep object

Sweep interpolation method, specified as one of the following:

• "direct" — Compute resonant frequency using all the specified frequencies.

• "interp" — Interpolate the sweep using rational fitting to compute resonant frequency with minimum possible set of frequency points within the specified frequency range.

• "interpWithGrad" — Interpolate the sweep using rational fitting with gradient calculations to compute resonant frequency with minimum possible set of frequency points within the specified frequency range.

• frequencySweep object — Interpolate the sweep using parameters such as error tolerance, number of frequency points, and number of iterations that you set in the frequencySweep object.

Frequency sweep interpolation methods use rational fitting to interpolate results over the frequency range defined by two or more specified frequency points.

When you use an interpolating sweep, the frequencies at which the resonantFrequency function computes and plots the results can differ from the frequencies in the input frequency vector. The effective set of frequencies depends on SweepOption:

• If SweepOption is a frequencySweep object, the effective frequencies are determined by its NumFreqs property.

• If SweepOption is "interp" or "interpWithGrad", the number of frequency points depends on how many frequencies you provide:

  • If you provide more than 30 frequencies, the sweep uses your frequencies directly.

  • If you provide 30 or fewer frequencies, the sweep uses the default of 100 points across the band.

Sweep Interpolation Methods

Method	When to Use	Trade-off
"direct"	Results at all specified frequencies	High computational cost; slow for large sweeps
"interp"	Faster results with automatic accuracy control and fewer simulations	No control over number of frequency points
"interpWithGrad"	Faster results with gradient information for optimization	Slightly more expensive than "interp"
frequencySweep object	Manual control over frequency resolution, error tolerance, and number of iterations	Requires manual tuning; no adaptive refinement

To use this feature, you need an RF Toolbox™ license.

Example: [fRES,sRES,S,sweepobj] = resonantFrequency(dipole,[10e6:1e6:180e6],Method="Sparameters",SweepOption="interp")

Data Types: string

Threshold — Threshold value for impedance or S₁₁

15 (default when Method is set to Impedance) | -10 (default when Method is set to Sparameters) | real scalar

Threshold value for impedance or S₁₁, specified as a real scalar in ohms when the Method is set to "Impedance" or a real scalar in dB when the Method is set to Sparameters.

Example: -12

Data Types: double

Z0 — Reference impedance to calculate S-parameters

50 (default) | positive real scalar

Reference impedance to calculate the S-parameters, specified as a positive real scalar in ohms. The default reference impedance is 50 ohms. This argument is valid only when the Method argument is set to Sparameters.

Example: 75

Data Types: double

PlotDataTips — Option to enable or disable data tips

true (default) | false

Option to enable or disable the data tips, specified as a logical true to enable or logical false to disable the data tips. By default, the data tips are enabled.

Example: Specifying PlotDataTips=false disables the data tips on the plot.

Data Types: logical

Output Arguments

fRES — Resonant frequency in Hz

positive scalar | positive vector

Resonant frequency in Hz of the specified antenna, returned as either positive scalar value for a single resonance or a positive vector for multiple resonances within the specified frequency sweep.

Example: 75.33e6

zRES — Impedance values corresponding to resonant frequencies

real scalar | complex scalar | real vector | complex vector

Impedance values corresponding to the resonant frequencies, returned as a real or complex scalar or vector. zRES is empty when there are no resonant frequencies within the specified frequency range. And zRES is a vector when multiple resonances are found within the specified frequency range.

Example: 75

Data Types: double
Complex Number Support: Yes

sRES — S11 values corresponding to resonant frequencies

numeric vector

S11 values corresponding to the resonant frequencies, returned as a complex vector in dB.

Data Types: double
Complex Number Support: Yes

Z — Impedance values over entire frequency range

complex vector

Impedance values over entire frequency range, returned as a complex vector in ohms.

Data Types: double
Complex Number Support: Yes

S — S₁₁ values over entire frequency range

complex vector

S₁₁ values over the entire frequency range, returned as a complex vector in dB.

Data Types: double

typRES — Resonance type

"Series" | "Parallel" | "Unclear"

Resonance type, returned as a string. The resonance type is either "Series", "Parallel" or "Unclear". When the reactance in the impedance plot approaches zero but does not cross it, resonance type is returned as "Unclear".

Example: "Parallel"

Data Types: string

sweepobj — Frequency sweep interpolation parameters

frequencySweep object

Frequency sweep interpolation parameters, returned as a frequencySweep object.

Tips

• Interpolating frequency sweeps may report results at frequencies that differ from the frequencies you specify. If you require results at exact frequencies, either use the default direct sweep, or set the NumFreqs property of the frequencySweep object greater than or equal to the number of frequencies you provide.

• When using the "interp" or "interpWithGrad" sweep options, provide more than 30 frequency points to have the sweep use your frequency resolution exactly; otherwise the sweep defaults to 100 points across the band.

Version History

Introduced in R2024a

R2026b: Use frequency sweep interpolation to calculate resonant frequency

Use the new SweepOption name-value argument to interpolate the frequency sweep for resonant frequency calculations. The interpolation methods use rational fitting or rational fitting with gradient information.