**Electrical memory effects**

Even when electrical memory effects of GaN HEMT are still not negligible compared to those of GaAs HEMT, but the benefit of high power density, high output impedance, high frequency, etc. of GaN HEMT can be used, when the device is accurately described including the memory effects by the device model. First of all, the extraction of model parameters should be done using multibias pulsed measurement data. In such a measurement process, the bias voltages of the transistor is pulsed starting from the so-called quiescent point to other bias points in the I-V characteristics and drain current Ids as well as S-parameters of that bias point are measured. Pulsed measurement has a significant advantage which is the isothermal measurement condition. The measured I-V characteristic of a pulsed measurement does not contain the self-heating of the transistor at high Vds and Ids as seen in DC measurement which is more familiar to the realistic operating condition. Moreover, quiescent point of pulsed measurement can be chosen equal to the operating point of the amplifier class of interest in order to create a device model which corresponds to the behavior of the device under realistic operating condition. In particular, the quiescent point dependent device model is necessary for a power device with significant trapping effects (see Fig. 9.). Theoretically, the dependence on quiescent point could be included into the model making the device model a general purpose one. However, as described above, this would increase the complexity and decrease the robustness of the model. Promising results of high power GaN HEMT have been published in 2004 showing the progress in GaN device technology in term of reduction of trapping effects where the DC measurement of I-V curves shows no significant difference in the level of drain current compared to a pulsed measurement with a quiescent point at high drain voltage region (Kikkawa et al, 2004). In such a case, the quiescent point dependence of the device model would not be so critical. For power transistor manufacturers, normally, only one device model is provided to the circuit designer. As a result, the model of a mature power device regarding trapping will offer more accurate results for arbitrary classes of amplifiers.

Fig. 9. Dependence of I-V characteristic of a GaN HEMT on quiescent point. The quiescent voltage was constant at a pinch-off value (no quiescent current) whereas the drain quiescent voltage Vdsq was varied.

#### **Knee walkout**

168 Wireless Communications and Networks – Recent Advances

Computer simulation of the performance belongs to a typical design flow of power amplifiers. As many as possible components in the amplifier circuit should be characterized and described by models in order to obtain accurate prediction of circuit's performance from the simulations. As the main component of a power amplifier, quality of power transistor model plays a significant role in the accuracy of circuit simulation. Especially for power amplifier design, nonlinearities of the device must also be described by the device model unlike for small signal amplifiers, where it is sufficient to have the device's S-

Even for one device technology, it is not practical to create a universal model which can describe the device's behavior under all operating conditions. In order to describe more effects and dependencies of the device's behavior on dynamic thermal and electrical conditions, more and more model parameters and nonlinear equations are required. In that case, the model would become very complex and long simulation time is needed. Though computational resource can be increased, complex device models suffer from poor robustness, that the simulation would be often terminated without convergence and reasonable results. For switched-mode power amplifiers e.g. class E, F, inverse F or D, a concept of using switch model in combination with the "on" state resistance Ron and output capacitance Cds instead of empirical transistor model exists (Negra et al, 2007). This simple model is capable of providing good trend of power and efficiency and of verifying switched-mode operating conditions. At this point, there exist some discussions regarding the accuracy of such switch model for switched-mode power amplifier applications. Especially for power devices with charge carrier trapping and thus, memory effects, the switch model is not able to describe such effects which can have influence in efficiency and

Even when electrical memory effects of GaN HEMT are still not negligible compared to those of GaAs HEMT, but the benefit of high power density, high output impedance, high frequency, etc. of GaN HEMT can be used, when the device is accurately described including the memory effects by the device model. First of all, the extraction of model parameters should be done using multibias pulsed measurement data. In such a measurement process, the bias voltages of the transistor is pulsed starting from the so-called quiescent point to other bias points in the I-V characteristics and drain current Ids as well as S-parameters of that bias point are measured. Pulsed measurement has a significant advantage which is the isothermal measurement condition. The measured I-V characteristic of a pulsed measurement does not contain the self-heating of the transistor at high Vds and Ids as seen in DC measurement which is more familiar to the realistic operating condition. Moreover, quiescent point of pulsed measurement can be chosen equal to the operating point of the amplifier class of interest in order to create a device model which corresponds to the behavior of the device under realistic operating condition. In particular, the quiescent point dependent device model is necessary for a power device with significant trapping effects (see Fig. 9.). Theoretically, the dependence on quiescent point could be included into the model making the device model a general purpose one. However, as described above, this would increase the complexity and decrease the robustness of the model. Promising results of high power GaN HEMT have been published in 2004 showing the progress in

output power of switched-mode amplifiers (Chalermwisutkul, 2008).

**3.1 GaN device modeling** 

**Electrical memory effects** 

parameter sets of a few bias points of interest.

In contrast to GaAs HEMT and MESFET, the knee voltage of a GaN HEMT depends on the gate voltage and the drain quiescent voltage. With high gate voltage, the knee of the I-V curve becomes more round than at lower gate voltage where the knee is relatively angular. In addition, the knee voltage is shifted to the right toward higher drain voltage when gate voltage is high. This so-called *knee walkout* effect observed only with GaN HEMT and not with GaAs HEMT or MESFET cannot be modeled with standard EEHEMT model. By adding dependency of the knee voltage on the gate voltage and the drain quiescent voltage, the knee region of the I-V curve with high gate voltage can be better described (see Fig. 10.). As a result more accurate power and efficiency simulation can be done (see Fig. 11.) (Chalermwisutkul, 2007).

Fig. 10. I-V curves fitting results without (left) and with (right) the description of the kneewalkout.

#### **Large signal behavioral model**

As discussed before, large signal model is required in order to describe nonlinearities of the power device. However, device modeling is a complex task which requires extensive experience of modeling engineers and special modeling software, so that power amplifier design engineers are mostly forced to rely on the large signal model provided by device's manufacturer. Due to progress in RF measurement techniques, a measurement system has been developed which allows measurement of the so-called X-parameters (Betts et al, 2011). Unlike with S-parameters, not only small signal behavior of the device can be described, but also nonlinearities arising under large signal conditions. In general, the input signal power is swept and the output response at the fundamental as well as at higher harmonics is measured. The measured information is then concluded into the Xparameter set which can be directly used in the circuit simulation software as the device's behavioral model. This kind of device modeling is very convenient and can be combined with source and load tuners to obtain load dependence of the X-parameters. In addition, the extracted behavioral model is accurate, robust and does not require large computational resource. However, the behavioral model cannot provide insights into physical properties of the device and the measurement setup is relatively expensive for small companies and educational institutions with low budget.

#### **Package modeling**

Packaged transistors comprise also parasitic components of the package and bond wires. These typical parasitic inductance and capacitance can compromise the performance of the amplifier circuit especially at high frequencies. For example, for class F amplifiers where short or open circuit must be provided at the drain node of the transistor at harmonic frequencies in order to shape the output current and voltage waveforms for high efficiency. Optimization for efficiency can be done best, if the package model of the transistor is known. The current and voltage waveforms which are optimized for minimum overlap should be presented at the internal drain node of the device inside the package and not at the external drain port (Schmelzer and Long, 2007).
