Matlab Analyze Rf Mixer

---
name: matlab-analyze-rf-mixer
description: >
  Analyze mixer spurious products and intermodulation using the mixerIMT object in RF Toolbox.
  Use when building intermodulation tables (IMT), visualizing spur charts, identifying spurious
  products at specific RF input frequencies, designing frequency plans, or comparing mixerIMT
  with modulator for rfbudget cascade analysis. Trigger on mixerIMT, intermodulation table, IMT,
  spur chart, spur analysis, spurious products, mixer spurs, frequency planning, spur-free zone,
  mixer nonlinearity, RF harmonic, LO harmonic, mixer spur visualization, OpenIF, open IF,
  IF planning, spur-free zone, multiband receiver, multiband transmitter.
license: MathWorks BSD-3-Clause
metadata:
  author: MathWorks
  version: "1.1"
---

# Mixer Intermodulation Analysis

Analyze mixer spurious products using the `mixerIMT` object. Build intermodulation tables, visualize spur charts, and integrate with `rfbudget` for cascade analysis.

## When to Use

- Building intermodulation tables (IMT) for mixer spur analysis
- Visualizing spur charts at specific RF input frequencies
- Identifying spurious products and designing frequency plans
- Using mixerIMT in rfbudget for cascade analysis with spur-aware mixer models

## When NOT to Use

- Simple cascade budgets without spur analysis -- use `modulator` via `matlab-create-rfbudget-elements`
- General rfbudget cascade analysis -- use `matlab-analyze-rf-budget`
- Composing mixer circuits with node wiring -- use `matlab-compose-rf-circuit`
- Processing complex baseband signals through mixers -- use `matlab-process-rf-baseband`

## Workflow

1. **Create mixer** — Construct `mixerIMT` with LO, ConverterType, and power levels
2. **Configure IMT** — Set custom intermodulation table or use defaults
3. **Visualize spurs** — Plot spur chart with `rfplot(m, fRF)`
4. **Integrate** — Add to `rfbudget` chain or `circuit` for cascade/circuit analysis

## `mixerIMT` vs `modulator`

Both model frequency converters, but serve different purposes:

| Feature | `modulator` | `mixerIMT` |
|---------|------------|------------|
| Gain specification | `Gain` property (direct) | `NominalOutputPower - ReferenceInputPower` |
| Nonlinearity | OIP3-based (poly model) | IMT table (arbitrary spur levels) |
| Spur visualization | No | Yes — `rfplot(m, fRF)` |
| Constructor accepts `Gain` | Yes | **No** — settable after construction but ignored by rfbudget |
| Use case | System-level cascade budgets | Spur analysis and frequency planning |

Use `modulator` for quick cascade budgets. Use `mixerIMT` when you need to model specific spurious products or visualize spur charts.

## Creating a mixerIMT

```matlab
m = mixerIMT('LO', 2.1e9, 'ConverterType', 'Down', 'NF', 10, 'Name', 'Mixer');
```

### Constructor Parameters

| Parameter | Default | Description |
|-----------|---------|-------------|
| `LO` | 1e8 | Local oscillator frequency (Hz) |
| `ConverterType` | `'Up'` | `'Down'` or `'Up'` conversion — **must set explicitly for down-conversion** |
| `NF` | 0 | Noise figure (dB) |
| `ReferenceInputPower` | -15 | Reference input power (dBm) |
| `NominalOutputPower` | -5 | Nominal output power (dBm) |
| `Model` | auto | `'mod'` (up) or `'demod'` (down) — set automatically from ConverterType |
| `Zin` | 50 | Input impedance (Ohm) |
| `Zout` | 50 | Output impedance (Ohm) |
| `IMT` | 3x3 default | Intermodulation table |
| `Name` | `'MixerIMT'` | Element name |

### Post-Construction Properties

These properties are read-write but **cannot be passed to the constructor**:

```matlab
m.OIP3 = 20;       % Output IP3 (dBm)
m.OIP2 = 40;       % Output IP2 (dBm)
```

**Do not set `m.Gain` manually.** Although `Gain` is a settable property, `rfbudget` ignores it — the budget gain is determined entirely by `NominalOutputPower` and `ReferenceInputPower`. Setting `m.Gain` has no effect on cascade results and can be misleading.

## Conversion Gain

Conversion gain in `rfbudget` is determined by `NominalOutputPower` and `ReferenceInputPower`. Although `Gain` is a settable property, `rfbudget` ignores it and computes gain from `NominalOutputPower - ReferenceInputPower`. Do not set `m.Gain` manually.

```
Budget gain = NominalOutputPower - ReferenceInputPower
```

```matlab
% This gives 10 dB conversion gain in rfbudget:
m = mixerIMT('ReferenceInputPower', -15, 'NominalOutputPower', -5, ...
    'LO', 2.1e9, 'ConverterType', 'Down', 'Name', 'Mixer');
% Budget sees: -5 - (-15) = 10 dB

% To get -6 dB conversion loss in rfbudget:
m2 = mixerIMT('ReferenceInputPower', -10, 'NominalOutputPower', -16, ...
    'LO', 2.1e9, 'ConverterType', 'Down', 'Name', 'Mixer');
% Budget sees: -16 - (-10) = -6 dB
```

## The IMT Table

The intermodulation table (IMT) is an MxN matrix where:
- **Rows** = RF harmonic order (row 1 = order 0, row 2 = order 1, ...)
- **Columns** = LO harmonic order (col 1 = order 0, col 2 = order 1, ...)
- **Values** = relative power in **dBc below the reference** (non-negative)
- `0` = reference level (desired output)
- `99` = fully suppressed

### Default Table

```matlab
m = mixerIMT;
disp(m.IMT);
%    99    99    99
%    99     0    99
%    99    99    99
```

The default 3x3 table has only the desired product (RF×1, LO×1) at row 2, col 2 with value 0 (reference). Everything else is suppressed (99).

### Custom IMT Table

```matlab
imt = 99*ones(5,5);       % Start with everything suppressed
imt(2,2) = 0;             % RF×1, LO×1: desired output (reference)
imt(2,1) = 20;            % RF×1, LO×0: RF feedthrough at -20 dBc
imt(1,2) = 15;            % RF×0, LO×1: LO feedthrough at -15 dBc
imt(3,2) = 30;            % RF×2, LO×1: 2RF-LO spur at -30 dBc
imt(2,3) = 25;            % RF×1, LO×2: RF-2LO spur at -25 dBc
m.IMT = imt;
```

**Gotcha:** The IMT must be a **real 2-D numeric matrix** (class `double`). Setting a cell array, 3-D array, complex matrix, or non-numeric type errors with "An Intermodulation Table must be real two dimensional matrix." Ensure `imt` is created with standard `double` operations (e.g., `99*ones(M,N)`).

**Gotcha:** IMT values must be **non-negative and ≤ 99** (they represent dBc below reference). Setting a negative value errors with "Value must be nonnegative." Setting a value > 99 errors with "Expected Spur table to be an array with all of the values <= 99." Using `inf` for "fully suppressed" also errors ("Value must be finite") — use `99` instead.

### Reading the IMT Table

| IMT Position | RF Order | LO Order | Spur Frequency (Down) |
|-------------|----------|----------|----------------------|
| `(1,1)` | 0 | 0 | DC |
| `(2,1)` | 1 | 0 | fRF (RF feedthrough) |
| `(1,2)` | 0 | 1 | fLO (LO feedthrough) |
| `(2,2)` | 1 | 1 | fRF - fLO (desired IF) |
| `(3,2)` | 2 | 1 | 2·fRF - fLO |
| `(2,3)` | 1 | 2 | fRF - 2·fLO |
| `(3,3)` | 2 | 2 | 2·fRF - 2·fLO |

## Spur Chart Visualization

```matlab
m = mixerIMT('LO', 2.1e9, 'ConverterType', 'Down', 'NF', 10, 'Name', 'Mixer');
figure;
rfplot(m, 2.4e9);   % Spur chart at fRF = 2.4 GHz
```

`rfplot(m, fRF)` displays a spur chart showing all intermodulation products at the specified RF input frequency, with their relative power levels.

**Gotcha:** `rfplot(m, fRF)` takes a **scalar** frequency, not a vector. Passing a frequency vector errors: "Value must be a scalar."

**Gotcha:** `rfplot(m)` with no frequency argument errors: "Not enough input arguments."

## Using in rfbudget

```matlab
lna = amplifier('Gain', 15, 'NF', 2, 'OIP3', 35, 'Name', 'LNA');
m = mixerIMT('ReferenceInputPower', -10, 'NominalOutputPower', -16, ...
    'NF', 10, 'LO', 2.1e9, 'ConverterType', 'Down', 'Name', 'Mixer');
ifAmp = amplifier('Gain', 20, 'NF', 4, 'OIP3', 30, 'Name', 'IFAmp');

b = rfbudget([lna m ifAmp], 2.4e9, -30, 10e6);
fprintf('Total Gain: %.2f dB\n', b.TransducerGain(end));
fprintf('Output Freq: %.3f GHz\n', b.OutputFrequency(end)/1e9);
```

After the mixer, the output frequency changes to the IF: `fIF = fRF - fLO` for down-conversion.

## Using in circuit

`mixerIMT` is a 2-port (4-terminal) element compatible with `circuit`:

```matlab
ckt = circuit('MixerCircuit');
add(ckt, [1 2 0 0], m);
setports(ckt, [1 0], [2 0]);
s = sparameters(ckt, freq);
```

## S2D Data Files

Load mixer characterization from an S2D file:

```matlab
m = mixerIMT('FileName', 'mixer_data.s2d', 'UseDataFile', true, ...
    'LO', 2.1e9, 'ConverterType', 'Down', 'Name', 'MeasuredMixer');
```

## OpenIF -- IF Frequency Planning

The `OpenIF` object finds spur-free intermediate frequencies in multiband receiver/transmitter architectures. Use it to identify open IF bands where no mixer spurs fall.

```matlab
hif = OpenIF(20e6);                    % 20 MHz IF bandwidth
imt1 = [99 99 99; 99 0 99; 99 99 99]; % Default 3x3 IMT
addMixer(hif, imt1, 2.4e9, 200e6, 'low', 20e6);   % RF center, RF BW, type, IF BW
addMixer(hif, imt1, 5.2e9, 200e6, 'low', 20e6);
show(hif);                             % Graphical spur-free zone display
report(hif);                           % Command-window summary
```

### `addMixer` Syntax

```matlab
addMixer(hif, imt, rfCenterFreq, rfBW, mixType, ifBW)
```

| Argument | Type | Description |
|----------|------|-------------|
| `hif` | OpenIF | The OpenIF object |
| `imt` | MxN double | Intermodulation table (same format as `mixerIMT.IMT`) |
| `rfCenterFreq` | scalar | RF center frequency (Hz) |
| `rfBW` | scalar | RF bandwidth (Hz) |
| `mixType` | char | `'low'` or `'high'` when IFLocation=`'MixerOutput'`; `'sum'` or `'diff'` when IFLocation=`'MixerInput'` |
| `ifBW` | scalar | IF bandwidth for this mixer (Hz) |

`'low'` means fIF = fRF - fLO (standard down-conversion); `'high'` means fIF = fRF + fLO.

| Property | Default | Description |
|----------|---------|-------------|
| `IFBW` | constructor arg | System-wide IF bandwidth (Hz) |
| `SpurFloor` | 99 | Maximum spur level to consider (dBc) |
| `IFLocation` | `'MixerOutput'` | `'MixerOutput'` or `'MixerInput'` |

`OpenIF` complements `mixerIMT`: use `mixerIMT` + `rfplot(m, fRF)` to visualize spurs at a single RF frequency; use `OpenIF` to find spur-free IF zones across an entire multiband architecture.

## Gotchas

1. **Do not set `m.Gain`** — Although `Gain` is settable, `rfbudget` ignores it and computes gain from `NominalOutputPower - ReferenceInputPower`. Setting it manually has no effect on the budget and can be misleading.
2. **Gain not in constructor** — `mixerIMT('Gain', -6)` errors. `Gain` cannot be passed as a constructor argument.
3. **IMT values must be 0-99** — They represent dBc below the reference (0 = reference, 99 = fully suppressed). Negative values error ("Value must be nonnegative"), values > 99 error ("values <= 99"), and `inf` errors ("Value must be finite"). Always use `99` for suppressed spurs, never `inf`.
4. **rfplot takes scalar frequency** — `rfplot(m, fRF)` requires a single frequency, not a vector.
5. **Default conversion gain is 10 dB** — `NominalOutputPower(-5) - ReferenceInputPower(-15) = 10 dB`. This is rarely what you want — set both explicitly.
6. **ConverterType sets Model automatically** — `'Down'` sets `Model='demod'`, `'Up'` sets `Model='mod'`.
7. **ConverterType defaults to `'Up'`** — If you omit `ConverterType`, the mixer performs up-conversion (`fOut = fRF + fLO`). Always set `'ConverterType', 'Down'` explicitly for down-conversion receivers.
8. **IMT must be a real 2-D double matrix** — Cell arrays, 3-D arrays, complex matrices, or non-numeric types error with "An Intermodulation Table must be real two dimensional matrix." Build with `99*ones(M,N)` then set individual entries.
9. **Clone elements before reusing in a second rfbudget** — An element object can only belong to one `rfbudget` at a time. Reusing it errors with "Element is already in another rfbudget." Use `clone(element)` to create an independent copy.

## Conventions

- Use `tiledlayout`/`nexttile` for multi-panel spur analysis figures
- Always label spur charts with the RF input frequency
- Set `ReferenceInputPower` and `NominalOutputPower` explicitly — do not rely on defaults
- Use `modulator` for simple cascade budgets; use `mixerIMT` when spur analysis matters

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