Electronica Analogica

Thermal Analysis of a Transistor
A.Cidronali, C.Accillaro, F.Zani,
Dept. Electronics and Telecommunications, University of Florence, V.S.Marta,3 Florence 50139 Italy,


By using the elctro-thermal-elctromagnetic model, it is possible to analyze the thermal effects in a power amplifier. The power amplifier, which has been taken into account, has been designed bymeans of a 4x150 GaAs PHEMT manufactured by the OMMIC foundry.
The scope of our analysis is to show thermal effects, which are obtained from the simulations, and how this effects are linked to the IM3. These effects are called nonlinear low frequency memory effects, which are generated by: thermal behavior, nonlinear behavior, and traps in the structure of the device. In the following, only thermalmemory effects are analyzed, while the traps have not been taken into account.
The instantaneous dissipated power determines the instantaneous rate of heat that is applied to the transistor. Furthermore, due to the finite mass of the component, thermal impedance includes a capacitive part in addition to the resistive one. Thermal resistance describes just the steady state behaviour, and thermalcapacitance is essential for description of the dynamic behaviour. In the figure below the thermal network models, is shown:


FIG.1: Thermal Circuit and Temperature expression.

As it is shown, from DC transistor characteristic, the temperature growing produce a drop of drain current and transconductance, as the electron mobility decrease with temperature. This effect that is the same assaying that source resistance is increased, so a lower VGS is obtained.

Without Thermal Effects


With Thermal Effects


FIG.2: DC Characteristic with thermal effects and without thermal effects.

In order to study the thermal memory effects, a two tone input signal is used, and it is defined in the following expression:




FIG.3: Device under Test

By using this kind ofanalysis, ranging the distance between two tone, it is possible to figure out the following Thermal behaviour.

FIG.4: Amplitude of temperature oscillation respect to frequency distance between tones

If we use a two tone input signal, we have a PRF,out modulated by a 2ωm tone, so a 2ωm temperature variation is obtained as well; the lower is the 2ωm from the thermal cut off frequency ωTH,the higher is the amplitude of the temperature modulation. As the RTH = 120 °C/W and Thermal Capacity CTH = 3.3x10-6 J/°C, the cut off of the thermal circuit is fTH = 400 Hz. The temperature changing produce a: IDS,dc and gm variation with a 2ωm frequency, so a Pdc variation and hence a Pdiss is obtain as well, this mechanism is valid as far as the equilibrium stationary condition has beenreached.

FIG.5: Dynamic Thermal behaviour

The Pdc variation, caused by temperature variation, generates a 2ωm electrical tone, which generates a IM3 by thermal origin, which is mixed with IM3 by electrical origin. In the following, some calculation steps, are used to describe, in an analytic manner, the mixed between IM3 thermal memory effects, and IM3 and nonlinear memory effects.

SimplifiedAnalysis

If the following expansion in term of Taylor series related to iDS,RF(t) is taken into account:

it is possible to write the output voltage, in terms of electrical nonlinear effects, and thermal memory effects, and for more simplicity the output voltage can be rewritten as:

if we consider the first order transconduttance :

where the factor “ a “is related to the amplitude oftranscoduttance variation with temperature, and its value is between (0,1), as it can be deduced from the physical description of the thermal behaviour of the device described above. Hence it is possible to write:


the same things is done for the second order transconduttance. Regard the third order transconduttance, only electrical nonlinear effects have been taken into account, because...