# Crystal

Model stable resonator

Passive Devices

## 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.

## Basic Assumptions and Limitations

The Crystal block models only the fundamental crystal vibration mode.

## Dialog Box and Parameters

Parameterization

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.

Series resonance, fs

Crystal series resonant frequency. This parameter is only visible when you select `Series resonance data` for the Parameterization parameter. The default value is `32.764` kHz.

Parallel resonance, fa

Crystal parallel resonant frequency that corresponds to operating with a parallel load capacitance specified by the Load capacitance, CL parameter. This parameter is only visible when you select ```Parallel resonance data``` for the Parameterization parameter. The default value is `32.768` kHz.

Motional inductance, L1

Inductance that represents the mechanical mass of the crystal. This parameter is only visible when you select ```Equivalent circuit parameters``` for the Parameterization parameter. The default value is `6.742e+03` H.

R1 parameterization

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.

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

Quality factor, Q

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

The default value is `9e+04`.

Equivalent series resistance, R1

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

The default value is `15` kΩ.

Motional capacitance, C1

Capacitance that represents crystal mechanical stiffness under load. The default value is `0.0035` pF.

Load capacitance that corresponds to the Parallel resonance, fa parameter value. This parameter is only visible when you select `Parallel resonance data` for the Parameterization parameter. The default value is `12.5` pF.

Shunt capacitance, C0

Electrical capacitance between the two crystal electrical connections. The parameter value must be greater than zero. The default value is `1.6` pF.

Initial voltage

The output voltage at the start of the simulation when the output current is zero. The default value is `0` V.

## Ports

The block has the following ports:

`+`

Positive electrical port

`-`

Negative electrical port