# rfbudget

Create RF budget object and compute RF budget results for chain of 2-port elements

## Description

Use the `rfbudget`

object to create an RF budget object and
compute the RF budget results for a chain of 2-port elements. In this RF chain, you can
use a 2-port element such as `amplifier`

,
`nport`

, or
`modulator`

. You
can also open the `rfbudget`

object in an RF
Budget Analyzer app and then export the completed circuit to RF Blockset™ for circuit envelope analysis.

## Creation

### Syntax

### Description

`rfobj = rfbudget`

creates an `rfbudget`

object, `rfobj`

, with default empty property values.

`rfobj = rfbudget(`

sets Elements, InputFrequency, AvailableInputPower, and SignalBandwidth properties and computes the RF budget
analysis. By default, if any of the input properties are changed, the object
recomputes results.`elements`

,`inputfreq`

,`inputpwr`

,`bandwidth`

)

`rfobj = rfbudget(___,`

sets the AutoUpdate property. You can use this syntax with any of the
previous syntaxes.`autoupdate`

)

`rfobj = rfbudget(Name=value)`

sets Properties using one
or more name-value arguments. You can specify multiple name-value
arguments.

## Properties

`Elements`

— RF budget elements

`[]`

(default) | RF budget object | array of RF budget objects

RF budget elements, specified as an RF budget object or an array of RF budget objects. Use an array of RF budget objects when you perform RF budget analysis on an RF chain.

This table lists supported RF budget elements you can use to design an RF chain.

Element Type | RF Budget Elements |
---|---|

Linear Elements | `attenuator` |

`rfantenna` | |

`rffilter` | |

`nport` | |

`seriesRLC` | |

`shuntRLC` | |

`phaseshift` | |

`txlineCoaxial` | |

`txlineCPW` | |

`txlineMicrostrip` | |

`txlineParallelPlate` | |

`txlineRLCGLine` | |

`txlineStripline` | |

`txlineTwoWire` | |

`txlineEquationBased` | |

`txlineDelayLossless` | |

`txlineDelayLossy` | |

Nonlinear Elements | `amplifier` |

`modulator` | |

`rfelement` | |

`mixerIMT` |

**Example: **```
a = amplifier; m = modulator; rfbudget(Elements=[a
m])
```

calculates the RF budget analysis of the amplifier and
modulator circuit.

`InputFrequency`

— Input frequency of signal

`[]`

(default) | nonnegative scalar or column vector in Hz

Input frequency of the signal, specified as a nonnegative scalar or column vector* (since R2023a)* of size
*M*-by-1 in Hz. *M* represents number
of frequencies. If the input frequency is a vector, then the RF budget
object analyzes each input frequency separately.

**Example: **`InputFrequency=2e9`

**Data Types: **`double`

`AvailableInputPower`

— Power applied at input of cascade

`[]`

(default) | scalar in dBm

Power applied at the input of the cascade, specified as a scalar in dBm.

**Example: **`AvailableInputPower=-30`

**Data Types: **`double`

`SignalBandwidth`

— Signal bandwidth at input of cascade

`[]`

(default) | scalar in Hz

Signal bandwidth at the input of the cascade, specified as a scalar in Hz.

**Example: **`SignalBandwidth=10`

**Data Types: **`double`

`AutoUpdate`

— Automatically recompute RF budget analysis

`true`

(default) | `false`

Automatically recompute the RF budget analysis by incorporating changes
made to the existing circuit, specified as `true`

or
`false`

.

Setting `AutoUpdate`

to `false`

turns
off automatic budget recomputation as parameters change. To compute the
budget result of an `rfbudget`

object when you set the
`AutoUpdate`

property to `false`

,
use the `computeBudget`

function.

**Example: **`AutoUpdate=false`

**Data Types: **`logical`

`Solver`

— Computation Method

`Friis`

(default) | `HarmonicBalance`

Computation method, specified as `Friis`

or
`HarmonicBalance`

. The `Friis`

solver
is faster and the `HarmonicBalance`

solver supports
computation of second-order nonlinearities such as OIP2.

When you set the `Solver`

type to
`HarmonicBalance`

, the tone and harmonic-dependent
properties are displayed.

**Note**

The `HarmonicBalance`

solver does not support
architectures where the input or output frequencies at any stage in the
cascade are nonzero and less than SignalBandwidth.

**Example: **`Solver='Friis'`

**Data Types: **`string`

`MaxHarmonics`

— Maximum number of harmonics for each tone in one- and two-tone HB analyses

`[]`

(default) | `positive integer`

*Since R2024a*

Maximum number of harmonics to use for each tone in one- and two-tone
harmonic balance (HB) analyses, specified as a positive integer. Use this
property for faster HB analysis and set `MaxHarmonics`

to
`[]`

to return to the default automatic determination
of harmonics.

**Example: **`MaxHarmonics=5`

#### Dependencies

To enable this property, set Solver to `HarmonicBalance`

.

**Data Types: **`double`

`MinHarmonics`

— Minimum number of harmonics for each tone in one- and two-tone HB analyses

`[]`

(default) | `positive integer`

*Since R2024a*

Minimum number of harmonics to use for each tone in one- and two-tone
harmonic balance (HB) analyses, specified as a positive integer. Use this
property to achieve higher-fidelity HB simulation in highly nonlinear
systems and set `MinHarmonics`

to `[]`

to return to the default automatic determination of harmonics.

**Example: **`MinHarmonics=5`

#### Dependencies

To enable this property, set Solver to `HarmonicBalance`

.

**Data Types: **`double`

`HarmonicOrder`

— Number of harmonics to use for all tones in HB analyses

`[]`

(default) | positive integer

Number of harmonics to use for one-tone harmonic balance (HB) analysis,
specified as a positive integer. For each two-tone analysis,
`max(3,HarmonicOrder)`

harmonics is used. Use the
default value for automatic determination of harmonics.

Use this property to

Accelerate the HB analysis by reducing the number of harmonics needed for a mildly nonlinear system.

Ensure harmonic balance accuracy by increasing the number of harmonics used in a highly nonlinear system.

#### Dependencies

To enable this property, set Solver to `HarmonicBalance`

.

**Data Types: **`double`

`OutputFrequency`

— Output frequencies

scalar | vector | matrix

This property is read-only.

Output frequencies in Hz, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

where *M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

**Data Types: **`double`

`OutputPower`

— Output power

scalar | vector | matrix

This property is read-only.

Output power in dBm, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

where *M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

**Data Types: **`double`

`TransducerGain`

— Transducer power gains

scalar | vector | matrix

This property is read-only.

Transducer power gains in dB, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

where *M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

**Data Types: **`double`

`NF`

— Noise figures

scalar | vector | matrix

This property is read-only.

Noise figures in dB, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

*M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

**Note**

If AvailableInputPower is very large, it can result in
negative `NF`

values during harmonic balance analysis
[1].

**Data Types: **`double`

`IIP2`

— Input-referred second-order intercept

scalar | vector | matrix

This property is read-only.

Input-referred second-order intercept (IIP2) in dBm, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

*M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

#### Dependencies

To compute IIP2 values, set Solver to `HarmonicBalance`

.

**Data Types: **`double`

`OIP2`

— Output-referred second-order intercept

scalar | vector | matrix

This property is read-only.

Output-referred second-order intercept (OIP2) in dBm, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

*M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

#### Dependencies

To compute OIP2 values, set Solver to `HarmonicBalance`

.

**Data Types: **`double`

`IIP3`

— Input-referred third-order intercept

scalar | vector | matrix

This property is read-only.

The Input-referred third-order intercept (IIP3) in dBm, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

*M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

**Data Types: **`double`

`OIP3`

— Output-referred third-order intercept

scalar | vector | matrix

This property is read-only.

The Output-referred third-order intercept (OIP3) in dBm, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

*M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

**Data Types: **`double`

`SNR`

— Signal-to-noise ratio

scalar | vector | matrix

This property is read-only.

Signal-to-noise ratio (SNR) in dB, returned as one of the following:

Scalar when

*M*and*N*=`1`

Vector when

*M*or*N*=`1`

Matrix when

*M*and*N*>`1`

*M* represents the number of
frequencies in the input and *N* represents the number of
stages in the cascade.

**Data Types: **`double`

`WaitBar`

— Display progress bar

true (default) | false

Display a progress bar with a cancel button during harmonic balance
analysis, specified as `true`

or
`false`

.

**Data Types: **`logical`

## Object Functions

`show` | Display RF budget object in RF Budget Analyzer app |

`computeBudget` | Compute results of RF budget object |

`exportScript` | Export MATLAB code that generates RF budget object |

`exportRFBlockset` | Export RF budget object to RF Blockset Model |

`exportTestbench` | Export RF budget object to RF Blockset measurement testbench model |

`rfplot` | Plot cumulative RF budget result vs. cascade input frequency and amplifier power characteristics |

`smithplot` | Plot measurement data on a Smith chart |

`polar` | Plot specified object parameters on polar coordinates |

## Examples

### Default RF Budget

Open a default RF budget object.

obj = rfbudget

obj = rfbudget with properties: Elements: [] InputFrequency: [] Hz AvailableInputPower: [] dBm SignalBandwidth: [] Hz Solver: Friis AutoUpdate: true

### RF Budget Analysis of Series of RF Elements

Create an amplifier with a gain of 4 dB.

a = amplifier(Gain=4);

Create a modulator with an OIP3 of 13 dBm.

m = modulator(OIP3=13);

Create an N-port element using `passive.s2p`

.

`n = nport('passive.s2p');`

Create an RF element with a gain of 10 dB.

r = rfelement(Gain=10);

Calculate the RF budget of a series of RF elements at an input frequency of 2.1 GHz, an available input power of –30 dBm, and a bandwidth of 10 MHz.

b = rfbudget([a m r n],2.1e9,-30,10e6)

b = rfbudget with properties: Elements: [1x4 rf.internal.rfbudget.Element] InputFrequency: 2.1 GHz AvailableInputPower: -30 dBm SignalBandwidth: 10 MHz Solver: Friis AutoUpdate: true Analysis Results OutputFrequency: (GHz) [ 2.1 3.1 3.1 3.1] OutputPower: (dBm) [ -26 -26 -16 -20.6] TransducerGain: (dB) [ 4 4 14 9.4] NF: (dB) [ 0 0 0 0.1392] IIP2: (dBm) [] OIP2: (dBm) [] IIP3: (dBm) [ Inf 9 9 9] OIP3: (dBm) [ Inf 13 23 18.4] SNR: (dB) [73.98 73.98 73.98 73.84]

Type the `show`

command at the command window to display the analysis in the **RF Budget Analyzer** app.

show(b)

### Plot Cumulative Output Power and Gain of RF System

Create an RF system.

Create an RF bandpass filter using the Touchstone® file `RFBudget_RF`

.

f1 = nport('RFBudget_RF.s2p','RFBandpassFilter');

Create an amplifier with a gain of 11.53 dB, a noise figure (NF) of 1.53 dB, and an output third-order intercept (OIP3) of 35 dBm.

`a1 = amplifier(Name='RFAmplifier',Gain=11.53,NF=1.53,OIP3=35);`

Create a demodulator with a gain of –6 dB, a NF of 4 dB, and an OIP3 of 50 dBm.

d = modulator(Name='Demodulator',Gain=-6,NF=4,OIP3=50, ... LO=2.03e9,ConverterType='Down');

Create an IF bandpass filter using the Touchstone file `RFBudget_IF`

.

f2 = nport('RFBudget_IF.s2p','IFBandpassFilter');

Create an amplifier with a gain of 30 dB, a NF of 8 dB, and an OIP3 of 37 dBm.

`a2 = amplifier(Name='IFAmplifier',Gain=30,NF=8,OIP3=37);`

Calculate the RF budget of the system using an input frequency of 2.1 GHz, an input power of –30 dBm, and a bandwidth of 45 MHz.

b = rfbudget([f1 a1 d f2 a2],2.1e9,-30,45e6)

b = rfbudget with properties: Elements: [1x5 rf.internal.rfbudget.Element] InputFrequency: 2.1 GHz AvailableInputPower: -30 dBm SignalBandwidth: 45 MHz Solver: Friis AutoUpdate: true Analysis Results OutputFrequency: (GHz) [ 2.1 2.1 0.07 0.07 0.07] OutputPower: (dBm) [-31.53 -20 -26 -27.15 2.847] TransducerGain: (dB) [-1.534 9.996 3.996 2.847 32.85] NF: (dB) [ 1.533 3.064 3.377 3.611 7.036] IIP2: (dBm) [] OIP2: (dBm) [] IIP3: (dBm) [ Inf 25 24.97 24.97 4.116] OIP3: (dBm) [ Inf 35 28.97 27.82 36.96] SNR: (dB) [ 65.91 64.38 64.07 63.83 60.41]

Plot the available output power.

```
rfplot(b,'Pout')
view(90,0)
```

Plot the transducer gain.

```
rfplot(b,'GainT')
view(90,0)
```

Plot S-parameters of an RF system on a Smith Chart and a Polar plot.

s = smithplot(b,1,1,'GridType','ZY');

p = polar(b,2,1);

### Harmonic Balance Solver for Nonlinear RF Budget Analysis

Create two modulators with output-referred second-order intercept set to 20 and available power gain set to 3.

m = modulator(Gain=3,OIP2=20,ImageReject=false,ChannelSelect=false); m2 = modulator(Gain=3,OIP2=20,ImageReject=false,ChannelSelect=false);

Create an RF budget object specifying the input frequency of the signal, power applied at cascade, and signal bandwidth. Select `HarmonicBalance`

as solver method to compute nonlinear effects such as IIP2 and OIP2.

`b = rfbudget([m m2],2.1e9,-30,100e6,Solver='HarmonicBalance')`

b = rfbudget with properties: Elements: [1x2 modulator] InputFrequency: 2.1 GHz AvailableInputPower: -30 dBm SignalBandwidth: 100 MHz Solver: HarmonicBalance WaitBar: true AutoUpdate: true Analysis Results OutputFrequency: (GHz) [ 3.1 4.1] OutputPower: (dBm) [ -27 -24] TransducerGain: (dB) [ 3 6] NF: (dB) [ 3.01 7.783] IIP2: (dBm) [ 17 4.457] OIP2: (dBm) [ 20 10.46] IIP3: (dBm) [ Inf Inf] OIP3: (dBm) [ Inf Inf] SNR: (dB) [60.96 56.19]

### Number of Harmonics in HB Analysis

Create an amplifier with a gain of 10 dB.

a = amplifier(Gain=10);

Create a modulator with an OIP3 of 13 dBm.

m = modulator(OIP3=13);

Create an N-port circuit element using `passive.s2p`

.

`n = nport('passive.s2p');`

Calculate the RF budget of a series of RF elements at an input frequency of 2.1 GHz, an available input power of –30 dBm, and a bandwidth of 10 MHz using HB analysis. Set the number of harmonics that the `rfbudget`

object should use for all the tones in HB analyses.

b = rfbudget([a m n],2.1e9,-30,10e6,... Solver="HarmonicBalance",HarmonicOrder=3)

b = rfbudget with properties: Elements: [1x3 rf.internal.rfbudget.Element] InputFrequency: 2.1 GHz AvailableInputPower: -30 dBm SignalBandwidth: 10 MHz Solver: HarmonicBalance HarmonicOrder: 3 WaitBar: true AutoUpdate: true Analysis Results OutputFrequency: (GHz) [ 2.1 3.1 3.1] OutputPower: (dBm) [ -20 -20 -24.6] TransducerGain: (dB) [ 10 9.996 5.396] NF: (dB) [-2.842e-14 -0.004353 0.3376] IIP2: (dBm) [ Inf Inf Inf] OIP2: (dBm) [ Inf Inf Inf] IIP3: (dBm) [ Inf 2.997 2.998] OIP3: (dBm) [ Inf 12.99 8.391] SNR: (dB) [ 73.98 73.98 73.64]

### Plot Phase and Group Delay of RF System

Create an RF bandpass filter using the Touchstone® file `RFBudget_RF`

.

f1 = nport('RFBudget_RF.s2p','RFBandpassFilter');

Create an amplifier with a gain of 11.53 dB, a noise figure (NF) of 1.53 dB, and an output third-order intercept (OIP3) of 35 dBm.

`a1 = amplifier(Name='RFAmplifier',Gain=11.53,NF=1.53,OIP3=35);`

Create a demodulator with a gain of –6 dB, a NF of 4 dB, and an OIP3 of 50 dBm.

d = modulator(Name='Demodulator',Gain=-6,NF=4,OIP3=50, ... LO=2.03e9,ConverterType='Down');

Create an IF bandpass filter using the Touchstone file `RFBudget_IF`

.

f2 = nport('RFBudget_IF.s2p','IFBandpassFilter');

Create an amplifier with a gain of 30 dB, a NF of 8 dB, and an OIP3 of 37 dBm.

`a2 = amplifier(Name='IFAmplifier',Gain=30,NF=8,OIP3=37);`

Calculate the RF budget of the system using an input frequency of 2.1 GHz, an input power of –30 dBm, and a bandwidth of 45 MHz.

b = rfbudget([f1 a1 d f2 a2],2.1e9,-30,45e6);

Show the analysis in the RF plot.

rfplot(b)

**Group Delay**

To plot the group delay, first plot the S11 data for the RF System.

rfplot(b,1,1)

Use the `Group Delay `

option on the plot graph to plot the group delay of the RF system.

**Phase Delay**

Use the `Phase Delay`

option on the plot graph to plot the phase delay of the RF System.

## Tips

The Touchstone file in the

`nport`

object must be passive at all specified frequencies. To make N-port S-parameters passive, use the`makepassive`

function.

## Algorithms

ABCD parameters are used in the computation of S-parameters of the cascade for Friis Solver. When S21 = 0, conversion to ABCD results in NaNs. For such cases, modifications to the S-parameters are made as follows:

### S_{21} = 0, S_{11} = -1, and S_{22} ≠ -1

Connected large resistance (R

_{p}= 10^{12}ohm) in parallel with the network.Connected small resistance (R

_{s}= 10^{-12}ohm) in series to the beginning of the network.

### S_{21} = 0, S_{22} = -1, and S_{11} ≠ -1

Connected large resistance (R

_{p}= 10^{12}ohm) in parallel with the network.Connected small resistance (R

_{s}= 10^{-12}ohm) in series after the network.

### S_{21} = 0, S_{22} = -1, and S_{11} = -1

Connected large resistance (R

_{p}= 10^{12}ohm) in parallel with the network.Connected small resistance (R

_{s}= 10^{-12}ohm) in series to the beginning of the network.Connected small resistance (R

_{s}= 10^{-12}ohm) in series after the network.

### S_{21} = 0

Connected large resistance (R

_{p}= 10^{12}ohm) in parallel with the network.

## References

[1] Roychowdhury, J., D. Long, and
P. Feldmann. “Cyclostationary Noise Analysis of Large RF Circuits with Multitone
Excitations.” *IEEE Journal of Solid-State Circuits*
33, no. 3 (March 1998): 324–36. https://doi.org/10.1109/4.661198.

## Version History

**Introduced in R2017a**

### R2024a: Control number of harmonics in HB simulation using `rfbudget`

object

You can now use the `rfbudget`

object to increase the number of
harmonics for higher fidelity HB simulation and reduce the number of harmonics for
faster HB simulation.

### R2023b: Recommended over `rfckt.cascade`

and `analyze`

`rfbudget`

is
recommend over `rfckt.cascade`

and `analyze`

because it enables you to:

Create an RF budget chain and compute the RF budget results for a chain of two-port elements. You can include linear and nonlinear elements in your chain. For more information, see Elements.

Compute gain, noise figure, IP2, and IP3 of cascaded RF elements using Friis and harmonic balance solvers and export the RF chain to RF Blockset and

`rfsystem`

for circuit envelope analysis.

### R2023a: `InputFrequency`

property now accepts only nonnegative scalar and vector values

Starting this release, you can specify the `InputFrequency`

property of the `rfbudget`

object as a nonnegative scalar or as a column vector of nonnegative values.

The `rfbudget`

object throws an error if you set the
`InputFrequency`

property to a negative value. Update the
property to a positive value in existing circuits designed using the
`rfbudget`

object to ensure accurate RF budget computations.

### R2022b: Specify number of harmonics to use for all tones in HB analysis

Specify the number of harmonics for all tones in HB analyses by setting the
HarmonicOrder property in the `rfbudget`

object.

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