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News:

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.

 

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Plotting Total RMS Noise Voltage

 

Circuit designers often need to know the relationship between the signal they are working with and the noise generated by their circuit. Noise analysis is useful in making sure that the expected signal is not buried by the noise that an electrical circuit generates with its resistances and semiconductor devices. One measurement that is useful is the total RMS noise voltage which can also be used to calculate the signal to noise ratio of a circuit. Measuring the total RMS noise voltage is a simple procedure in Micro-Cap. The simple resistor divider shown below will be used to demonstrate how the theory matches the simulation results.

Resistor divider circuit

The noise voltage spectral density (thermal noise) of a resistance is calculated through the well known equation:

Sqrt(4*k*T*R)

where k is Boltzmann's Constant, T is the temperature in Kelvin, and R is the resistance. This produces a result in units of volts per root Hertz. To calculate the total RMS noise voltage, the frequency bandwidth needs to be taken into account. The spectral density needs to be integrated over the bandwidth of interest. Since the noise voltage spectral density of a resistance is constant across all frequencies, the integrated equation can be simplified as:

Sqrt(4*k*T*R*B)

where B is the bandwidth. For the resistor divider circuit, the theoretical noise values are calculated using the following values:

k = 1.3807e-23
T = 300.15K (27C)
R = 500k (1Meg // 1Meg)
B = 19980 (20Hz to 20kHz)

The theoretical results for the resistor divider are:

Noise Voltage Spectral Density = 91.04nV/sqrt(Hz)
Total RMS Noise Voltage = 12.87uV

In Micro-Cap, the total RMS noise voltage of a circuit can be plotted using the following expression.

Sqrt(SD(Onoise**2))

Onoise is a Micro-Cap operator which represents the noise voltage spectral density of the circuit at the specified output node. The SD function will integrate the expression with respect to frequency in AC analysis. An AC analysis is run on the resistor divider circuit from 20Hz to 20kHz. The plot is displayed below.

Resistor divider noise results

Both the Onoise variable and the Sqrt(SD(Onoise**2)) have been plotted. Note that since the SD function performs a running integral of the expression, only the last value in the plot is important since the value at 20kHz will be the integrated value across the entire simulated bandwidth. As can be seen in the cursor tables of the plot, the simulated values are dead on with the theoretical values.

The resistor divider is a simplified example to show that the mathematics for the total RMS noise voltage expression work in Micro-Cap. This same expression can be used with any type of circuit that includes shot and flicker noise as well as thermal noise. To demonstrate this, the basic audio amplifier (Ref 1) shown below will be simulated.

Audio amplifier circuit

This audio amplifier is simulated from 1Hz to 100kHz. Both the Onoise and the total RMS noise voltage expressions are plotted. The results are shown below. The total RMS noise voltage across the simulated bandwidth for this audio amplifier is 54.968uV as shown in the cursor tables.

Thanks to Sigurd Ruschkowski for helping develop this technique to work with Micro-Cap.

Audio amplifier noise results

References
1) "Basic Audio Amplifier" - http://www.ecircuitcenter.com/Circuits_Audio_Amp/Basic_Amplifier/Basic_Audio_Amplifier.htm

 
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