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Home Assignment 2: Large Signal Modeling

Michael Winters & Jingjing ???: Chalmers University of Technology

I Introduction and Method

The aim of the assignment is to generate a large signal model of a GaAs HEMT with a gate width of 100 musing the transistor model of developed at Chalmers by Prof. Angelov. This is essentially done in threesteps. The S-parameters of the device are given, and generally the small-signal model is used as a startingpoint for extracting the large signal parameters in the Chalmers model (this model is very commonly usedwhen one is attempting to model the behavior of HEMT devices at microwave frequencies).

First the extraction of the extrinsic (parasitic) resistances {Rs, Rd, Rg}, inductances {Ls, Ld, Lg} and ca-pacitances {Cps, Lpg, Lpgd} are extracted using the method of Dambrine et. al. and Gao et. al. (Problem1 and 2). Then one must extract some of the intrinsic small signal parameters using the method of Rorsmanet. al. They are as follows.

Rj : The gate to drain series resistance

Cgd: The intrinsic gate to drain capacitance

Ri: The gate to source series resistance

Cgs: The intrinsic gate to source capacitance

Rds: The drain to source series resistance

Cds: The intrinsic drain to source capacitance

gm: The device transconductance

: The phase difference between current and voltage. v(t) = i(t)gmei

These values are generally attained from the measured S-parameters. By converting the S-parametersmeasured for varying gate and drain voltages (and frequency) to Y-parameters, it is possible to calculateall of the above parameters directly using the Rorsman model. The results of this small-signal parameterextraction are shown in section 2 and 3.

The essential motivation of a large signal model is that the intrinsic device parameters (specifically theintrinsic capacitance) tend to vary as a function of applied gate bias Vgs and the applied drain bias Vds.Generally one may write for the input and output waveforms.

Vin = Vgs + Vin(t)

Iin = Igs + Iin(t)

Vout = Vds + Vout(t)Iout = Ids + Iout(t)

In a small-signal situation, one assumes the following: Vin(t) |Vgs|, Iin(t) |Igs|, Vout(t) |Vds|, andIout(t) |Ids|. Essentailly, the magnitude of the input and output waveforms do not significantly alterthe gate and drain biases. In this situation, one can treat the intrinsic parameters of the device as beingconstant. When the input and output waveforms are large compared to the gate and drain biases, thevariation of the intrinsic device parameters must be taken into account. The core idea is that forlarge input and output signals, the input and output waveforms see a different a device with

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different intrinsic parameters as a function of time (e.g. the operating point of the device isdynamically changing.) For a simple example, consider the following.

Vin = V0 + V0 sint

At t = 0, the device has a gate bias of V0, while at t =2

the gate bias is 2V0. Because the intrinsicparameters of the transistor (such as capacitances) are different at t = 0 and t =

2, a large signal

model is required. Generally, the effect of this is to introduce non-linearity into the device such that if theinput wave is sinusoidal, the output wave will pick up harmonics and not look sinusoidal. The periodicity(i.e. the frequency) of the input and output waves will generally be preserved but the shape of the outputwave will tend to vary with increasingly large signals. Input and output waves are shown for various inputpowers in the final section of this report.

Using the parameters extracted from the Rorsman small-signal model as a base, it is possible to extractthe large signal model parameters with the application of Angalovs model. One uses the small-signalmodel to obtain a rough estimate of the large signal parameters. These are then optimized using ADS, inorder to tune the model to the fitted data. Generally, this begins with the extraction of the device DCparameters IIpk0, Vpks, P1, Ij , Pg, Vjg . These are the essential parameters which govern the shape of theDC-characteristics of the device (Note: thermal effects must also be taken into account). The results of

this extraction are shown in 4.

The core of the large signal model lies in determining the shape of the curves of the intrinsic gate-sourceand gate-drain capacitaces respectively {Cgs, Cgd}. Using the S-parameter measurements, it is possibleto plot the variation of the {Cgs, Cgd} as a function of the gate bias. By measuring the capacitance atpinch-off {Cgspi, Cgdpi} and at the inflection point of the capacitance curve {Cgs0, Cgd0}, the Chalmersmodel can build curves representing the variation of {Cgs, Cgd} with gate and drain bias. The results ofthis extraction are shown in 5

Finally, one can optimize and test the model by comparing it with load-pull data using a very simplepower amplifier design. The load and source impedances at which the output power of the device is amaximum (at 3GHz) is used to design matching networks. It is then possible to see the accuracy of the

model when compared with simulated data using Harmonic Balance simulations. Finally, the input andoutput waveforms and load-lines can be plotted while the input power is varied, allowing one to see how thedevice introduces nonlinearity into the output waveforms as a result of the variations in device propertieswith the input waveform.

The core results of the large-signal extraction are presented in the following sections. For the sake ofbrevity, minimal description is given. A full understanding may be obtained in the references given withthe assignment.

II Extraction of the Extrinsic Impedances

Here are ploted the extracted parasitic resistances, inductances, and capacitances as a function of frequency.

The real and imaginary parts of the Z-parameters are also shown.

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III Extraction of the Intrinsic Device Parameters

Here is shown the extraction of the small-signal DC parameters using the Rorsman method. The simulationschematics is shown as well. Here the drain voltage is swept from Vds = 2V 20V and the gate voltageis swept from Vgs = 6V 0V. Plots show the small signal parameters plotted against drain voltage forfixed gate voltages.

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IV Extraction of the DC IV Characteristics

The plots below show the IV-Characteristic following the optimization of the Chalmers large-signal modelDC characteristics. The top plot shows Vds plotted against Ids for fixed Vgs. The second plot shows Vgsplotted against Ids for fixed Vds. The red dots indicate the measured data while the smooth lines representthe results of the model with the parameters optimized. Note that thermal effects are taken into accountin the modeling.

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V Extraction of the Large Signal Capacitance Parameters

Here is shown the method of extraction of the capacitances needed to complete the large signal model. Theto plots show Cgd and Cgs plotted against gate bias. The markers show (very approximately) the valuesneeded for the large signal model (the pinch-off and inflection point capacitances) for both Cgd and Cgs.

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VI A Simple Power Amplifier: Output Power

The model parameters from the previous extraction are then entered into the model (shown below). Then asimple matching network (inspired by the load-pull) data and bias-tee is introduced and 100 order harmonicbalance simulations are performed. The output power vs. input power (dBm) is plotted for the measureddata (red dots) and the simulated data (blue line). The amplifier is designed for maximum output powerat 3Ghz.

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VII A Simple Power Amplifier: Load Lines and Output Waveforms

Finally plotted below are the input and output waveforms for the amplifier designed as above. The inputpower is swept from 8dBm 20dBm with the intention of showing the non-linearity in the output powerfor high input powers. It is also useful to note that the load lines are elliptical for low power indicatingthat the current and voltage waves at the output are not in phase.

As the input power is increased, the load lines become quasi-elliptical demonstrating the introduction ofharmonics as the amplifier is driven into compression. This is also most clear in the highest amplitudeoutput power traces for voltage and current (they begin looking only quasi-sinusoidal). It is furtherimportant to note that different harmonics see different input and output impedances in the amplifier, andthus get distorted differently. This is due to the fact that reactive elements within the model are a functionof both frequency and gate bias (as discussed in the introduction).

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