Thermal Analysis of a Transistor

Thermal Analysis of a TransistorA.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 by means 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 thermal memory 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 thermal capacitance 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 as saying 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 of analysis, 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 2m tone, so a 2m temperature variation is obtained as well; the lower is the 2m from the thermal cut off frequency TH, 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 2m 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 been reached.

FIG.5: Dynamic Thermal behaviour

The Pdc variation, caused by temperature variation, generates a 2m 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.

Simplified Analysis

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 of transcoduttance 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 the frequency value, which is obtained from mixer between electrical and thermal effects, doesnt generate the IM3 products.

Finally the expression of the IM3 products is:

As gm1, gm2,gm3 have a trend, which is reported in the figure, it is possible to say that the IM3 products generated by thermal effects are in opposing to the IM3 products generated by electrical memory effects.

(a)

(b)

(c)FIG.6: gm1,gm2,gm3 trend respect to gate source Voltage, a) represent gm1 trend, b) represent gm2 trend, a) represent gm3 trend.

As can be seen from the figure above, the gm2 variation with temperature, can be neglected, so it is possible to suppose that In the following figure the simulation results are shown, and as can be seen, the analytic previsions, which are obtained by simplified mathematical analysis, are coherent, with simulation results. The temperature changes have repercussion on electrical parameters of the transistor that influence the amplifiers behaviour. Instantaneous transistor junction temperature variation depends on instantaneous dissipated power and, consequently, on the input signal time variation. As result, the dependency of the complex gain of high PAs on junction temperature can be considered as a source of nonlinearity. In the figure are reported the simulation result, related to the IM3 products generated from thermal and electrical memory effects, which are compared with the IM3 products memory effects generated by electrical memory effects only. All result is obtained by changing the frequency spacing between the two tone input signal.As can be seen the level of IM3 generated by a pure electrical nonlinearity effect, is independent from the two tone frequency spacing.

IM3(0-3 m) Electrical ME

IM3(0+3 m) Electrical ME

IM3(0-3 m) Thermal ME

IM3(0+3 m) Thermal ME

FIG.7: Comparison between IM3 products by taking into account of thermal effects and without thermal effects.

If we consider a different transistor, like HBT, it is possible to observe another IM3 trend, because the thermal behaviour is different respect to the HFET behaviour. An increasing of temperature produce an increasing of collector current, hence the dissipated power is increased as well. In the following figure are reported the DC characteristic, temperature dependent, and a comparison between HFET IM3, HBT IM3.

FIG.7: Comparison between IM3 HBT behaviour and IM3 HFET behaviour.

This effect is due to the a factor, where it has a value between (-1,0), because thermal effects in Bipolar transistor is related to an increasing of Transconductance with temperature.

References

[1] N.Le.Gallou, J.M. Nebus, E. Ngoya, H.Buret Analysis of low frequency memory and influence on solid state HPA intermodulation characteristic, 2001, IEEE MTT-S Digest.

[2] S.Boumaiza, Fadhel, Ghannouchi Thermal memory effects modelling and compensation in RF power amplifiers and Predistorsion linearizers , IEEE Transaction on Microwave Theory and techniques, Vol.51 No.12, December 2003.