Spectrum Software
Industrial Strength Simulation




Spectrum Software has released Micro-Cap 11, the eleventh generation of our SPICE circuit simulator.

For users of previous Micro-Cap versions, check out the new features available in the latest version. For those of you who are new to Micro-Cap, take our features tour to see what Micro-Cap has to offer.




Modeling Impedance with Tabular Data in AC Analysis


Quite a few components can be modeled in Micro-Cap by simply simulating their impedance characteristics. One method to model a complex impedance is to combine resistors, inductors, and capacitors together until the impedance versus frequency curve matches the expected results. This method can be very time consuming if done by hand. If the model is to be simulated in an AC analysis, an easier method is described in this article that will use data triplets of the frequency, impedance magnitude, and impedance phase to represent the complex impedance.

One device where modeling the complex impedance is crucial for an AC simulation is a loudspeaker. A typical speaker will specify a nominal impedance such as eight ohms. This only describes the standard impedance of the speaker. Over different frequencies, the speaker impedance may vary drastically from this nominal value. At this point, it will be assumed that the impedance magnitude and phase versus frequency for the loudspeaker has already been obtained through measurement of a physical device, from a data sheet, or through another program. For this example, the impedance curve defines the impedance characteristics for a fifteen inch, eight ohm loudspeaker from 1Hz to 20kHz. This curve was derived from data in the book "High Performance Audio Power Amplifiers" by Ben Duncan. Once the data is available, it should be converted into a .define statement and placed in the Text page of a schematic. Part of the define statement for the specified loudspeaker is as follows:

.define Speaker
+ 1.000000,  6.642448,  7.075845
+ 1.050764,  6.648317,  7.075845
+ 1.104105,  6.654794,  7.430443
+ 1.160153,  6.661941,  7.802316
+ 1.219047,  6.669827,  8.192229
.. .
+ 16406.252669,  70.373163,  85.429172
+ 17239.098286,  73.939376,  85.649411
+ 18114.222406,  77.689242,  85.859090
+ 19033.771253,  81.632330,  86.058708
+ 20000.000000,  85.778745,  86.248742

This define statement creates the symbolic variable Speaker. The + signs are used as a continuation character to tell Micro-Cap that the following lines are still associated with the Speaker variable. Each data triplet is defined as:

Frequency, Impedance magnitude, Impedance phase

Alternatively, the real and imaginary values of the impedance can also be used in this method by defining the triplet as:

Frequency, Real impedance, Imaginary impedance

The components within Micro-Cap that can read in data in this type of format are the Laplace table sources. The Laplace table source comes in four varieties: LTIofI - current controlled current source, LTIofV - voltage controlled current source, LTVofV - voltage controlled voltage source, and LTVofI - current controlled voltage source. For modeling impedance, only the LTVofI and the LTIofV sources are applicable. Due to the data types specified in the Speaker define statement, the Laplace source which will be used in this instance is the LTVofI. This Laplace source measures the current through its input, looks up the transfer function in the defined table, and produces the resultant voltage output. For impedance, the source should be wired so that the measured input current is the current through its own voltage output. This creates the function:

V = I * Table transfer function

where I and V are both assigned to the Laplace source output so that the table transfer function is the direct equivalent of the complex impedance. This method models the voltage drop that would exist if the impedance was present in the circuit. Should a LTIofV source be used instead, the voltage inputs need to be wired to measure the voltage across the current source output as this method would model the current flow that would exist if the impedance was present. The table data would also have to be transformed into the following:

Frequency, 1/Impedance magnitude, - Impedance phase

since the table transfer function should now be the equivalent of the conductance. An example circuit displaying the use of the LTVofI impedance method is displayed below.

Loudspeaker impedance example

In the schematic, an AC source of magnitude 1 is the input into an INA134 audio differential line receiver. The output of the INA134 is then fed into the input of a BUF634 high speed buffer. The Sense pin of the INA134 is connected to the output of the BUF634. This configuration provides an output current boost to the circuit. The LTVofI component that models the loudspeaker impedance is connected to the output of the BUF634 device. Note that the Laplace source has been wired so that it is measuring the current through itself. The Laplace source has its attributes defined as:

FREQ = Speaker

The FREQ attribute defines the table values for the source. In this case, the Speaker symbolic variable has been entered which will use the define statement that was created previously and stored in the Text page of the schematic. The KEYWORD attribute defines the type of data that is specified in the table. Mag indicates that the magnitude value is true magnitude and Deg specifies that the phase value is in degrees.

The AC analysis for this circuit is displayed below. The impedance of the speaker output is calculated by using the expression V(Out)/I(H1). The top plot shows the magnitude of the impedance and the middle plot shows the phase of the impedance. The impedance curves show the general impedance characteristics of a loudspeaker. These two waveforms match precisely with the data that was specified within the Speaker table definition. The bottom plot displays the output current that is generated through the LTVofI source.

Loudspeaker impedance AC simulation

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