Why Network Analyzer Signal Levels Affect Measurement Results

Jan 1, 2011 12:00 PM
Steven M. Sandler, Chief Engineer, AEi Systems Tom Boehler, Senior Engineering Specialist, AEi Systems, Charles E. Hymowitz, Managing Director, AEi Systems

When analyzing transistors, there is a finite allowable signal level that provides accurate results, which is due to a phenomenon related to the large signal effects of semiconductor junctions.

Find a downloadable version of this story in pdf format at the end of the story.

When measuring a circuit or device with a network analyzer, engineers generally inject a signal and believe that the measured results reflect that of a “small-signal” AC measurement. Many of us have been taught to keep the signals “very small.” But what does that mean exactly? This article will answer the question “how small is very small” and additionally ‘is the reason that the signal must be so small due to an issue with my network analyzer?” We will also discuss why we do not see the effects of signal amplitude in corresponding SPICE simulations.

SPICE-based circuit simulators use partial derivatives to perform small-signal AC analysis; therefore, they are not sensitive to the independent voltage sourceís signal level; regardless of the AC magnitude, the results are linearized and scaled. So, in a physical test environment, how large can the injected signal be before it significantly impacts the measurement?

We can start by first characterizing a semiconductor device we want to measure. We will use a transistor as an example because a transistor has a known emission coefficient (N=1), thus removing N as an unknown parameter. The voltage of a silicon junction is given by:

Where:

ID = Forward biased current

IS = Saturation current

N = Emission coefficient

VT = Thermal voltage (K×T/Q) = 0.026V @ 25°C

Rs = Series resistance

Differentiating VF with respect to ID results in the junction impedance:

Where:

Rj = Small signal junction impedance

If we assume the junction temperature of the device to be 25°C, knowing the Boltzmann constant, K, and the elementary charge, Q, we can solve VT as shown by:

We can also assume ID is much greater than IS, and Rj is much greater than Rs; therefore:

Next, we can derive an equation that defines the maximum input power allowed to obtain an impedance result that is within 10% of the exact small signal solution as a function of the DC bias, the signal's source impedance (R_in), and the device emission coefficient:

(See equation 5)

We know the emission coefficient of a transistor is 1, and our network analyzer source impedance is specified to be 50 Ω, so we can determine the maximum allowable input power level for a range of bias conditions:

Pin_dBm(0.0001,50,1) = -30.69 dBm

Pin_dBm(0. 001,50,1) = -22,47 dBm

Pin_dBm(0.005,50,1) = -11.027 dBm

Pin_dBm(0. 01,50,1) = -5.387dBm

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