# Crystal

Stable resonator

Libraries:
Simscape / Electrical / Passive

## Description

The Crystal block represents the electrical characteristics of a crystal. The following figure shows the equivalent circuit model of the Crystal block.

You specify the equivalent circuit parameters for this model when you set the Parameterization parameter to ```Equivalent circuit parameters```.

• The capacitor C0 corresponds to the capacitance you specify in the Shunt capacitance, C0 parameter.

• The capacitor C1 corresponds to the capacitance you specify in the Motional capacitance, C1 parameter.

• The inductor L1 corresponds to the inductance you specify in the Motional inductance, L1 parameter.

• The resistor R1 corresponds to the resistance you specify in the Equivalent series resistance, R1 parameter.

Most datasheets specify crystal frequency rather than inductance, so the block optionally accepts frequency data.

• When you set the Parameterization parameter to `Series resonance data`, the block uses the following relationship to calculate L1 from the series resonant frequency:

`${f}_{s}=\frac{1}{2\pi \sqrt{{L}_{1}{C}_{1}}}$`

Where fs is the Series resonance, fs parameter value.

• When you set the Parameterization parameter to `Parallel resonance data`, the block uses the following relationship to calculate L1 from the parallel resonant frequency:

`${f}_{a}=\frac{1}{2\pi \sqrt{{L}_{1}{C}_{1}\left({C}_{0}+{C}_{L}\right)/\left({C}_{1}+{C}_{0}+{C}_{L}\right)}}$`

Where:

• fa is the Parallel resonance, fa parameter value.

• CL is the Load capacitance, CL parameter value.

Some datasheets specify quality factor rather than equivalent series resistance, so the block optionally accepts quality factor data. When you set the R1 parameterization parameter to ```Quality factor Q```, the block uses the following relationship to calculate R1 from the quality factor:

`$Q=\frac{2\pi f{L}_{1}}{{R}_{1}}$`

Where Q is the Quality factor, Q parameter value.

Note

The R1 parameterization parameter is only visible when you select `Series resonance data` or ```Parallel resonance data``` for the Parameterization parameter.

## Assumptions and Limitations

• The Crystal block models only the fundamental crystal vibration mode.

## Ports

### Conserving

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Electrical conserving port associated with the crystal positive voltage.

Electrical conserving port associated with the crystal negative voltage.

## Parameters

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Select one of the following methods for block parameterization:

• `Series resonance data` — Provide series resonant frequency and capacitance data for the crystal. This method is the default.

• `Parallel resonance data` — Provide parallel resonant frequency and capacitance data for the crystal.

• `Equivalent circuit parameters` — Provide electrical parameters for an equivalent circuit model of the crystal.

Crystal series resonant frequency.

#### Dependencies

This parameter is visible only when you select ```Series resonance data``` for the Parameterization parameter.

Crystal parallel resonant frequency that corresponds to operating with a parallel load capacitance specified by the Load capacitance, CL parameter.

#### Dependencies

This parameter is visible only when you select ```Parallel resonance data``` for the Parameterization parameter.

Inductance that represents the mechanical mass of the crystal.

#### Dependencies

This parameter is visible only when you select ```Equivalent circuit parameters``` for the Parameterization parameter.

Select one of the following methods for series resistance parameterization:

• `Equivalent series resistance R1` — Provide the resistance value directly. This is the default method.

• `Quality factor Q` — Provide the quality factor that the block uses to calculate the resistance value.

#### Dependencies

This parameter is visible only when you select ```Series resonance data``` or ```Parallel resonance data``` for the Parameterization parameter.

Crystal quality factor. This parameter is only visible when you make one of the following selections:

• `Series resonance data` for the Parameterization parameter and `Quality factor Q` for the R1 parameterization parameter

• `Parallel resonance data` for the Parameterization parameter and `Quality factor Q` for the R1 parameterization parameter

#### Dependencies

This parameter is visible only when you select:

• `Series resonance data` for the Parameterization parameter and `Quality factor Q` for the R1 parameterization parameter

• `Parallel resonance data` for the Parameterization parameter and `Quality factor Q` for the R1 parameterization parameter

Motional damping term. This parameter is only visible when you make one of the following selections:

• `Series resonance data` for the Parameterization parameter and `Equivalent series resistance R1` for the R1 parameterization parameter

• `Parallel resonance data` for the Parameterization parameter and `Equivalent series resistance R1` for the R1 parameterization parameter

• `Equivalent circuit parameters` for the Parameterization parameter

#### Dependencies

This parameter is visible only when you select:

• `Series resonance data` for the Parameterization parameter and ```Equivalent series resistance R1``` for the R1 parameterization parameter

• `Parallel resonance data` for the Parameterization parameter and ```Equivalent series resistance R1``` for the R1 parameterization parameter

• `Equivalent circuit parameters` for the Parameterization parameter

Capacitance that represents crystal mechanical stiffness under load.

Load capacitance that corresponds to the Parallel resonance, fa parameter value.

#### Dependencies

This parameter is visible only when you select ```Parallel resonance data``` for the Parameterization parameter.

Electrical capacitance between the two crystal electrical connections.

The output voltage at the start of the simulation when the output current is zero.

## Version History

Introduced in R2009a