Measuring Transistor ft

16 Jul 2008 • 5 minute read

So let’s consider a practical example of creating test benches and performing measurements, starting with how to characterize a transistor. A couple of questions to consider before starting are:

What parameters do you want to measure?
What types of test benches are required to measure these parameters?

Let’s start by considering how to measure the ft of a transistor, ft is a standard figure of merit used by analog designers to evaluate a transistor’s performance. Later we will consider how to measure some other common transistor parameters fmax, Noise Figure, as well as, measuring device stability.

First, let’s review the meaning of ft. It is defined as the unity gain frequency of a transistor’s short circuit current gain. The first point is that we need to measure the short circuit current gain so ideally the output terminal, collector [drain] of the transistor will be connected to a power supply. The next point is that we need to calculate the current gain of the transistor. For Virtuoso Analog Design Environment users, the Virtuoso Visualization and Analysis waveform calculator can be used to perform this measurement. To calculate ft, plot the current gain by dividing the collector [drain] current by the base [gate] current and then using the cross function to find the unity gain frequency. An example of calculating ft, is shown in Figure 1.

Figure 1: Measuring Transistor f_t
When creating a simulation test bench the natural place to start is the actual measurement test bench. To measure ft, an RF network analyzer can be used to measure the s-parameters and then the s-parameters can be converted into h-parameters. By plotting the h21, the ft can be estimated by extrapolating the unity gain frequency of the h21. This approach works well in the lab because wideband shorts do not exist in the real world. So RF measurements need to be performed with input and output matching and a result s-parameters are the natural method for characterizing transistors. One issue when testing in the lab is the need for separate bias and RF sources. Typically these sources are isolated with a bias T. In place of a bias T, we will use an inductor [pass the bias voltage at dc] and a capacitor [pass the RF input at frequency].

Figure 2: Emulating the Network Analyzer Setup to Measure h21
Using the lab test bench introduces some complexity that is not required when performing the measurement in simulation. By taking advantage of the “ideal” nature simulation, the test bench can be simplified. In simulation, we can create a perfect short using a voltage source. The voltage source provides bias and acts as a short circuit replacing the output matching circuitry in the original test bench. The RF input has been replaced by a current source with ac magnitude of 1 so the current gain can be directly measured. The input bias is still controlled by setting a dc voltage, see Figure 3.

This test bench works well when measuring ft for a single bias condition. However, it is difficult to sweep the bias current of the transistor as can be done in the lab with a bias generator.

Figure 3: Enhanced Test bench with an Output Short

The next enhancement is to replace the bias voltage source and resistor with a diode connected transistor and a current source to set the bias current of the device under test [DUT], see Figure 4. Using a diode connected transistor to generate the bias voltage allows the bias current to be easily controlled. The dc bias and the RF input are still isolated by the pseudo bias T. This change to the test bench allows a designer to characterize the effect of bias current on ft so the transistor can be operated at its maximum ft.

Figure 4: Improved ft Testbench
Another enhancement to the test bench would be to replace the inductor and the capacitor used in the pseudo bias-T, shown in Figure 5. Virtuoso Spectre circuit simulator provides users analysis-dependent switches that can be set to open and closed depending on the analysis to be performed. This allows the designer to use the same test bench to perform multiple tests, for example, NF, fmax, etc.

Figure 5: Using analysis dependent switches
The test bench I use to measure ft is even simpler, in which the bias network [diode, analysis dependent switches, and RF source] is replaced by an ideal current mirror. The current mirror provides feedback to stabilize the bias point. The current source that sets the bias current is also RF input source the bias T is eliminated. BTW, you might recognize this type of circuit, it is called a Wilson current mirror, shown in Figure 6.

Figure 6: My ft Test bench

To review the test bench development process, we started by replicating the test bench we used in the lab in simulation. Then the test bench was optimized by tuning it to take advantage of the “ideal” nature of a SPICE simulator. Along the way we made several improvements to the measurements process:

Directly measured the ft, eliminating the need to generate the s-parameters and then calculate the h-parameters.
Added the ability to sweep the bias current so plots of ft vs. Ic can be generated, see Figure 7.

Figure 7: Plot of ft vs. Ic

In closing, I hope that this example of creating a test bench and making measurements will be useful for you. Please let me know what you think.

Best Regards,
Art Schaldenbrand

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