3. Multiband, Multistandard Amplifiers for Mobile Base Stations
4.4. Model Parameter Extraction for Additional Effects
ranges of the characteristic is not required for a specific application. For improved model quality for the region of the characteristic that accommodates the active load line of the application, only the bias points of interest may be selected and taken into account for the direct optimization. With this application oriented nonlinear modeling, the errors can be reduced to less than 5% for the bias points of interest.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 5 10 15 20 25 Ids (A ) Vds(V) Fitted Measured
Figure 4.9.: Direct optimization for parameter extraction of large signal model; Device: GaN HEMT with 1 mm gate width; here: optimization of the I-V characteristic.
4.4. Model Parameter Extraction for Additional Effects.
As described in above, multibias S-parameters and DC data are used for the model parameter extraction. However, these measured data are not able to provide informa- tion about the device behavior under some operating conditions. Equations describing output conductance dispersion, forward conduction of gate source diode and gate drain breakdown are integrated with the model. However, to extract the model parameters de- scribing these effects, additional measurement types are required, which will be discussed in the following.
4.4.1. Modeling of Gate Source Diode
As the amplitude of the RF-input-signal increases, the device nonlinearities become more noticeable. The main source of the large signal nonlinearities is the signal clipping in the pinch-off region where Vgs has a large negative value and at the region of a high positive
Vgs value due to the forward conduction of the gate source diode. Under this condition,
large gate current flows and further increase of the drain current is not possible. If Vgs
is steadily increased, the device will be destroyed due to high gate current. This effect is simply described by the diode characteristic equation
52 Chapter 4. Large Signal Transistor Modeling for Power Amplifier Design Igs(Vgs) = IS·(exp Vgs N·VT − 1) (4.3)
which is also described by the standard EEHEMT1 model with the reverse saturation current IS and the diode-ideality-factor N as model parameters. The voltage VT is de-
pendent on the temperature with VT = kT/qe. In order to extract these parameters, a
special measurement of the gate current Igs as a function of gate voltage is required. For
this purpose, the gate voltage Vgs is swept whereas the drain port is left floating. From
the measured diode characteristic, the parameters can be extracted. An example of a gate source diode characteristic is depicted in figure 4.10.
−1.5 −2 −2.5 −3 0 0.5 1 1.5 −10 −9 −8 −7 −5 −4 −3 −2 −1 −6 −1 −0.5 lo g| Igs /A | Vgs(V) Measured Fitted
Figure 4.10.: Characteristic of the gate source diode of a GaN HEMT with 1 mm gate width at the ambient temperature of 25 °C, extracted parameters: IS = 1.0577·10
−5A,
N = 6.638.
4.4.2. Dispersion of the Output Conductance at Low Frequency
From the measurements of I-V characteristics, it is obvious that the drain current mea- sured with pulsed bias voltages differs from the one measured with DC bias voltages. This difference is caused by various effects e.g. self-heating and trapping effects which lead to the dispersion of the device output conductance. This can be confirmed with a measurement of S22 in a low frequency range from hundreds of kHz to tens of MHz. Theso-called low frequency dispersion is observed in all GaN HEMTs investigated in this work and also in mature GaAs-based HEMTs [53]. Figure 4.11 shows a Smith chart plot of S22 measured with a network analyser for the frequency range from 300 kHz to 200
MHz, where a kink is observed at approx. 20 MHz. Considering the output impedance, the kink of S22 shows that the impedance decreases with the increasing frequency.
To describe this dispersion effect, model equations of the drain current are separated for the case of DC and RF signals which require separate sets of parameters. The index “AC” of the parameters e.g. in GMMAXAC indicates that the parameters are
4.4. Model Parameter Extraction for Additional Effects. 53
S22
300 kHz 200 MHz
≈ 20 MHz
Figure 4.11.: Measurement of S22 in the frequency range from 300 kHz to 200 MHz
showing the output conductance dispersion at approx. 20 MHz; Device: GaN HEMT with 1 mm gate width; Bias point: Vgs = −1.8V, Vds = 9.6 V.
designated for the description at high frequencies. The difference of drain current at DC and high frequency is described by an additional current source IDB at the drain side
of the device, so that the drain current IAC
DS is equal to IDCDS + IDB at high frequencies.
The resistance RDB and the capacitance CBS are the parameters which define the corner
frequency fDispersion of the dispersion effect determined from the measurement of S22 in a
low frequency range as shown in figure 4.11, where IDB starts to contribute to the output
current. The corresponding equation is
fDisp =
1 2πCBSRBD
. (4.4)
With a fixed, large RBD value of 100 kΩ to minimize the influence of CBS on the output
capacitance, CBS can be determined from equation 4.4.
4.4.3. Gate Drain Breakdown
By increasing the drain voltage from zero, the drain current increases linearly if Vds is
low. After the saturation voltage has been reached, the drain current does not change significantly since the channel is pinched off at the drain side due to the high field in the gate drain region or even drops as a consequence of the self-heating. However, as the drain source voltage is increased steadily, the electric field between gate and drain becomes so large that the gate drain path breaks and the device is destroyed by the steep current increase. In general, increasing the gap between gate and drain leads to a higher breakdown voltage. The gate-drain breakdown process can be measured by setting the gate voltage lower than the pinch-off voltage and increasing the drain voltage carefully (see figure 4.12). The equations describing this effect can be found in appendix B with the corresponding parameters KBK, VBR, NBR, IGD and IBR (see appendix A). For power
54 Chapter 4. Large Signal Transistor Modeling for Power Amplifier Design 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0 10 20 30 40 50 60 70 80 90 100 Vds(V) Ids (m A )
Figure 4.12.: Gate drain breakdown measurement at Vgs = −7 V of a 1 mm GaN HEMT.
4.4.4. Thermal Effects
Since the efficiency of a device can not reach 100% in the reality, the device dissipates power in form of heat. The temperature increase can cause current degradation as ob- served in figure 4.3. The I-V characteristic measured with DC bias voltages in continuous mode shows a current drop in the saturation region of the characteristic in contrast to a measurement in pulsed mode. This effect is usually significant at a high current and a high drain supply voltage. In this region, power dissipation is high (P = I·V) which
leads to a high temperature increase due to self-heating. Alteration of the device channel temperature due to the change of the power dissipation is a time delayed process which can be described in an averaged fashion with the equivalent electric circuit shown in figure 4.13.
Ith Rth Cth Vth
Figure 4.13.: Equivalent circuit for the description of self-heating effect.
The thermal current source Ithand the thermal voltage Vthhave no electrical meaning but
represent the power dissipation and the difference between the change of the temperature respectively. Similarly, the thermal resistance Rth and the thermal capacitance Cth form
the thermal time constant τth of the self-heating with
τth = Rth·Cth. (4.5)
After the temperature-difference has been determined, the large signal parameters are modified to add temperature-dependency. The temperature-dependent model parame-