# BJT S-Parameter Measurement and Analysis Using UTMOST

Introduction

The extraction of BJT DC and capacitance parameters
is relatively straight forward and easy to perform using sophisticated
parameter extraction software such as **UTMOST**. However, if
the BJT devices in question are going to be used in high frequency
circuit applications then the SPICE parameters associated with the
BJT small-signal AC model will have to be determined. In order to
enable accurate and efficient AC device characterization, S-parameter
measurements [1] are usually made and analyzed. A network analyzer
is normally employed to measure the required S-parameter data. This
article will describe how **UTMOST** can be used to perform S-parameter
measurements and to extract the required AC Gummel-Poon BJT model
parameters.

High Frequency BJT Modeling

If a BJT device is required to operate in a circuit at frequencies above its 3-dB frequency then accurate estimates of the parameters associated with the BJT AC model are necessary. The SPICE implementation of the AC small-signal model is basically a linearization of the large-signal model. Therefore, it is imperative that the BJT DC, capacitance, emitter, base and collector resistance parameters are extracted before any attempt is made to determine the AC parameters. Three elements are added to the BJT DC model in order to complete the AC model. These additional elements are the variable base resistor, the base-emitter diffusion capacitor, and the base-collector diffusion capacitor. These elements effectively add an RC delay to the frequency response of the small-signal model. This is true in both the forward and reverse modes of device operation. Device forward and reverse AC current gain and input impedance are normally determined using S-parameter measurements in order to characterize these three extra AC model elements. The Gummel-Poon SPICE parameters associated with the additional AC model elements are the TF (forward transit time), XTF (fitting coefficient for TF), ITF (coefficient for TF current dependence), VTF (coefficient for TF voltage dependence), PTF (excess phase), and TR (reverse transit time).

The task of taking successful S-parameter measurements is notoriously difficult. Measurements are make from the MHz to GHz frequency range where calibration methodologies are required to mask out the imperfections associated with the test measurement equipment, the test fixtures, and even the test structures in cases where on-wafer S-parameter measurements are being made. It is vital that systematic errors relating to impedance mismatch, isolation, and leakages, as well as the characteristic frequency response of the measurement equipment, probes, test fixtures, and test structures are taken into account using calibration and de-embedding techniques.

S-Parameter Measurement Example

Prior to S-parameter measurement it is necessary
to calibrate the measurement system. This usually necessitates the
configuration of a network analyzer with a DC analyzer which will
provide the DC biasing. The **UTMOST** AC calibration screen
is opened and the power, attenuation, and calibration kit coefficients
entered. The calibration kit coefficients are normally supplied
by the probe manufacturers. Figure 1 shows a example of an **UTMOST**
AC calibration screen.

Figure 1. An example of an UTMOST AC calibration screen.

More precise calibration is possible in **UTMOST**
using 2-step or 3-step de-embedding methods. In the 2-step de-embedding
technique an "open device" structure, having the same layout as
the device under test but without the metal lines being connected,
is measured after the standard open, short, 50 ohm load, and thru
calibration tests. In the 3-step de-embedding technique a "stort
device" test is added. The structure on which this test is measured
will have the same pad layout as the device under test but the metal
lines will be shorted. If "open device" or "short device" structures
are not available then only the standard calibration tests can be
performed.

After the calibration is finished the calibration
results must be verified by using the **UTMOST** `"Verify
Cal."` button. This is done for each of the S-parameter types.
Depending on the standard structure which is connected to the network
analyzer, a successful calibration will be indicated by a clean
point or semi-circle on the network analyzer screen.

A common-emitter biasing configuration was chosen
for the S-parameter measurements in this example. The **UTMOST**
measurement routine used was the `FT_CE` routine which measures
all four S-parameters (S11, S12, S21, and S22) for each bias chosen.
The measurement setup screen used in this example is shown in Figure
2.

Figure 2. The FT_CE measurement setup screen.

Different biasing sweep options are available for
selection from this screen. The scheme chosen here was the "`VBE,
VCE const`"option. This option sweeps the VBE bias while keeping
VCE constant at the user-defined supplied value. This option also
allows for the fact that the input impedance of most network analyzers
(i.e. 1MOhm) can cause a significant portion of the device's base
current to leak to ground. A reference Gummel-Poon measurement is
made and this data is used to make sure that the correct corresponding
values of base and collector current are used during the S-parameter
measurements. More details of this biasing option, as well as the
other remaining biasing options, can be found in the *UTMOST Extractions
Manual Volume 2.* From each DC bias point a plot of H21 versus
frequency is plotted on a Log scale and the cut-off frequency is
extracted. An example of one of these plots is shown in Figure 3.

Figure 3. A H21 versus frequency plot for a single bias.

Parameter Extractions Using S-Parameters

The extracted cut-off frequencies are collected
for each bias and the UTMOST `FTPlots` routine is used to
plot FT versus IC curves as shown in Figure 4.

Figure 4. FT versus IC curves
displayed by the `FTPlots` routine.

The `FTPlots` routine can also be used to
extract the TF, XTF, ITF, and VTF Gummel-Poon SPICE model parameters.
The `FTPlots` Fit option extracts initial estimates for these
parameters. As mentioned earlier in this article, the DC, resistance,
and depletion junction capacitance model parameters should be extracted
prior to the extraction of any of the AC model parameters. After
the initial extraction is completed, optimization techniques can
be used to refine these parameter values. **UTMOST** uses an
internal FT model to allow the optimization of SPICE parameters
to the FT versus IC characteristics. Although junction capacitance
parameters such as CJC and CJE may affect the FT predictions in
certain low current regions of operations, the optimization of such
parameters using the FT versus IC data is not recommended. The TF
parameter should be kept close to .
(maximum FT)/2 and XTF should normally be close to unity. The ITF
parameter models the FT roll-off current in a similar manner as
IKF does in the DC model. The value of ITF is usually greater than
IKF. VTF is used to model the FT variation with the collector-emitter
bias (VCE). Parameter optimization can also be performed directly
on S-parameter measurements using the the `s_plots` routine.
Figure 5 shows an example of S-parameter measured and simulated
curves for a single bias point. The optimization of AC model parameters
using H, Y, or Z-parameter data is also allowed by **UTMOST**.
In all of these cases the external SPICE simulator (i.e. **SmartSpice**)
is used to simulate the modeled data. **UTMOST** will automatically
convert S-parameter data to H, Y, or Z-parameter data where appropriate.

Figure 5. S-Parameters versus
frequency plots displayed by

the s-plots routine. (Measured ++++++ Simulated _______).

Conclusions

The methodology by which S-parameter measurements
can be taken with **UTMOST** and used for the extraction of Gummel-Poon
AC model parameters was described in this article. The measurement
of good S-parameter data and the subsequent extraction of AC model
parameters is usually a non-trivial task but accurate AC model parameters
are required for high-frequency BJT circuit applications.

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**References**

[1] S-Parameter Design, Hewlett Packard Application Note 154.