Crystal

Stable resonator.

blockType: AcausalElectricPowerSystems.Passive.Crystal

Path in the library:

/Physical Modeling/Electrical/Passive/Crystal

Description

Block Crystal represents the electrical characteristics of the crystal. The figure below shows an equivalent block diagram. Crystal.

crystal 1

The parameters of the equivalent circuit for this model are set when setting for the parameter Parameterization values Equivalent circuit parameters.

The capacitor corresponds to the capacity specified in the parameter Shunt capacitance, C0.
The capacitor corresponds to the capacity specified in the parameter Motional capacitance, C1.
The inductor coil corresponds to the inductance specified in the parameter Motional inductance, L1.
The resistor corresponds to the resistance specified in the parameter Equivalent series resistance, R1.

Most technical descriptions specify the frequency of the quartz resonator, not the inductance, so the unit additionally receives frequency data.

If for the parameter Parameterization the value is set Series resonance data, the block uses the following relation to calculate from the resonant frequency of the sequential circuit:

where — parameter value Series resonance, fs.
If for the parameter Parameterization the value is set Parallel resonance data, the block uses the following relation to calculate from the resonant frequency of the parallel circuit:

where
- — parameter value Parallel resonance, fa;
- — parameter value Load capacitance, CL.

Some technical specifications specify the Q-factor rather than the equivalent series resistance, so the unit optionally accepts Q-factor data. If for the parameter R1 parameterization the value is set Quality factor Q the block uses the following formula to calculate by quality:

where — parameter value Quality factor, Q.

To use the parameter R1 parameterization, set for the parameter Parameterization meaning Series resonance data or Parallel resonance data.

Assumptions and limitations

Block Crystal simulates only the main oscillation mode of the crystal.

Ports

Conserving

# + — positive terminal
electricity

Details

A non-directional electrical port connected to the positive voltage of the crystal.

Program usage name

p

# − — negative terminal
electricity

Details

A non-directional electrical port connected to the negative voltage of the crystal.

Program usage name

n

Parameters

# Parameterization — parameterization of the block
Series resonance data | Parallel resonance data | Equivalent circuit parameters

Details

Select one of the following block parameterization methods:

Series resonance data – specify the data on the resonant frequency of the serial circuit and the crystal capacity. This method is used by default.
Parallel resonance data – specify the data on the resonant frequency of the parallel circuit and the crystal capacity.
Equivalent circuit parameters – specify the electrical parameters of the equivalent crystal circuit.

Values	`Series resonance data` \| `Parallel resonance data` \| `Equivalent circuit parameters`
Default value	`Series resonance data`
Program usage name	`parameterization`
Evaluatable	Yes

# Series resonance, fs — the resonant frequency of the sequential circuit of the crystal
Hz | kHz | MHz | GHz

Details

The resonant frequency of the sequential circuit of the crystal.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Series resonance data.

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`32.764 kHz`
Program usage name	`f_series`
Evaluatable	Yes

# R1 parameterization — parameterization of the series resistance
Equivalent series resistance R1 | Quality factor Q

Details

Choose one of the following methods for parameterizing the series resistance:

Equivalent series resistance R1 – specify the resistance value directly. This method is used by default.
Quality factor Q – specify the Q factor that the block uses to calculate the resistance value.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Series resonance data or Parallel resonance data.

Values	`Equivalent series resistance R1` \| `Quality factor Q`
Default value	`Equivalent series resistance R1`
Program usage name	`series_resistance_parameterization`
Evaluatable	Yes

# Equivalent series resistance, R1 — dynamic damping
Ohm | mOhm | kOhm | MOhm | GOhm

Details

A component of dynamic damping.

Dependencies

To use this parameter, set

for the parameter Parameterization meaning Series resonance data, and for the parameter R1 parameterization meaning Equivalent series resistance R1;
for the parameter Parameterization meaning Parallel resonance data, and for the parameter R1 parameterization meaning Equivalent series resistance R1;
for the parameter Parameterization meaning Equivalent circuit parameters.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`15.0 kOhm`
Program usage name	`R`
Evaluatable	Yes

# Motional capacitance, C1 — dynamic capacity
F | pF | nF | uF | mF

Details

A container reflecting the mechanical rigidity of the crystal under load.

Units	`F` \| `pF` \| `nF` \| `uF` \| `mF`
Default value	`0.0035 pF`
Program usage name	`C_motional`
Evaluatable	Yes

# Shunt capacitance, C0 — shunting capacity
F | pF | nF | uF | mF

Details

The electrical capacity between the two electrical connections of the crystal.

Units	`F` \| `pF` \| `nF` \| `uF` \| `mF`
Default value	`1.6 pF`
Program usage name	`С_shunt`
Evaluatable	Yes

# Initial voltage — Initial output voltage
V | uV | mV | kV | MV

Details

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

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`0.0 V`
Program usage name	`V_start`
Evaluatable	Yes

# Quality factor, Q — crystal quality factor

Details

The quality of the crystal.

Dependencies

To use this parameter, set

for the parameter Parameterization meaning Series resonance data, and for the parameter R1 parameterization meaning Quality factor Q;
for the parameter Parameterization meaning Parallel resonance data , and for the parameter R1 parameterization meaning Quality factor Q.

Default value	`90000.0`
Program usage name	`Q`
Evaluatable	Yes

# Parallel resonance, fa — resonant frequency of the parallel crystal circuit
Hz | kHz | MHz | GHz

Details

The resonant frequency of the parallel circuit of the crystal, corresponding to operation with a parallel load capacity, determined by the parameter Load capacitance, CL.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Parallel resonance data.

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`32.768 kHz`
Program usage name	`f_parallel`
Evaluatable	Yes

# Load capacitance, CL — load capacity
F | pF | nF | uF | mF

Details

Load capacity corresponding to the parameter value Parallel resonance, fa .

Dependencies

To use this parameter, set for the parameter Parameterization meaning Parallel resonance data.

Units	`F` \| `pF` \| `nF` \| `uF` \| `mF`
Default value	`12.5 pF`
Program usage name	`C_load`
Evaluatable	Yes

# Motional inductance, L1 — dynamic inductance
H | nH | uH | mH

Details

The inductance, which is the mechanical mass of a crystal.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Equivalent circuit parameters.

Units	`H` \| `nH` \| `uH` \| `mH`
Default value	`6742.0 H`
Program usage name	`L`
Evaluatable	Yes