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e R1 Tj ... Fig. 2. Network representation of the model Z(t) with the parameters depending on the power Rys. 2. Reprezentacja obwodowa modelu Z(t) z parametrami uzależnionymi od mocy The efficiencies of the controlled sources existing in Fig. 2 are expressed by du i i Ci = C i ⋅ (1) dt e = R ⋅ i (2) where C i and R i are described by the formulae given in Section III. The values of the derivative du/dt are calculated with the use of DDT function. Estimation of the model parameters The practical realization of the algorithm described in illustrated on the example of the MESFET transistor CRF24010F and of the Schottky diode SDP10S30. Both the considered devices have operated without any heat-sink at the ambient temperature T a = 20 o C. Ri [K/W] Ci [J/K] 10 p th i C1 e R2 100 10 1 i C2 Ri = i Ri i CN e RN 0,1 0 0,5 1 1,5 2 2,5 3 3,5 p th [W] 100 10 1 0,1 0,01 0,001 0,0001 R 6 C 6 C 4 C 5 R 4 R 5 R 2 R 3 CRF24010F R 1 CRF24010F C 1 C 2 C 3 0,00001 0 0,5 1 1,5 2 2,5 3 3,5 p th [W] Fig. 3. Measured (points) and calculated (lines) dependences R i (p th ) and C i (p th ) for the transistor CRF24010F Rys. 3. Zmierzone (punkty) i obliczone zależności R i (p th ) oraz C i (p th ) dla tranzystora CRF24010F Tabl. 1. Values of the parameters existing in Eqs (3), (4) for the transistor CRF24010F Tab. 1. Wartości parametrów występujących we wzorach (3), (4) dla tranzystora CRF24010F i C i0 a i1 a i2 b i1 b i2 R i0 d i1 d i2 e i1 e i2 p i1 p i2 p i3 p i4 1 10 -5 10 -5 -3 10 0.2 0.3 0.7 0.5 4 0.5 2 2 1 2 0.003 0.9 -0.7 1.5 3 23 -0.3 -0.7 35 78 2 3 -2 -3 3 0.13 0.9 -0.7 2.5 5 1.65 0.3 0.7 1 24 2 3 2 1 4 0.27 0.9 -0.7 2.5 6 2.5 3 3 0.7 3 2 3 1 1 5 0.4 0.9 -0.7 2.5 6 700 -0.15 -0.85 35 90 2 3 -2 -4 6 9.2 0.9 -0.7 2.5 6 163 -0.15 -0.85 35 90 2 3 -2 -4 According to the point a) of the algorithm, the courses of the transient thermal impedance Z(t) at the device dissipated power in the wide range from are measured. Then, according to the point b) of the algorithm, the dependences R i (p th ) and C i (p th ) are obtained with the use of the algorithm ESTYM. These dependence represented by points are shown in Fig. 3 for the transistor CRF24010F. According to the point c) of the algorithm, the following description of the dependence C i (p th ) and R i (p th ) is proposed ⎡ ⎛ p ⎞ ⎛ ⎞⎤ th − pi 1 pth − p i 2 C = ⋅ ⎢ + ⋅ ⎥ (3) ⎜− + ⋅ ⎣ ⎟ ⎜− ⎟ i Ci0 1 a exp a exp i1 i 2 ⎝ bi 1 ⎠ ⎝ b i 2 ⎠ ⎦ ⎡ ⎛ p ⎞ ⎛ ⎞⎤ th − pi3 pth − p i 4 R = ⋅ ⎢ + ⋅ ⎥ (4) ⎜− + ⋅ ⎣ ⎟ ⎜− ⎟ i Ri 0 1 d exp d exp i1 i 2 ⎝ ei 1 ⎠ ⎝ e i 2 ⎠ ⎦ where C i0 , a i1 , a i2 , b i1 , b i2 , d i1 , d i2 , e i1 , e i2 , R i0 , p i1 , p i2 , p i3 , p i4 are the model parameters. The values of these parameters, obtained by matching the measurements and calculations results (the fourth stage in the algorithm) are collected in Table 1 for the transistor CRF24010F. To estimate the correctness of the approximation procedure, the dependences R i (p th ) and C i (p th ) were calculated with Eqs. (3) and (4). The calculation results are shown in Fig. 3 with the use of solid lines. As seen the points and the solid lines fit well. Verification of the model accuracy To verify the accuracy of the presented model, in Figs. 4 and 5 the measured (solid lines) and calculated (dotted lines) courses of the transient thermal impedance of the diode SDP10S30 at five values of the device dissipated power (Fig. 4) and of the transistor CRF24010F at six values of the device dissipated power are compared. As seen, the measured and calculated results fit well, which confirms good accuracy of the proposed model. To justify the necessity of using the device nonlinear thermal model, the following experiment has been performed. The time dependences of the inside temperature T j (t) of the investigated transistor CRF24010F obtained with the use of both the nonlinear (Fig. 2) and the classical linear device thermal models of the device dissipated power of the various shapes are calculated. As it was shown in [15], the considered dependence obtained from the nonlinear model differ from the other ones even more than 30%. It is worth mentioning, that using the nonlinear thermal model in the d.c. thermal analysis is not justified, because there is only one parameter – the thermal resistance existing in the model. So, it is necessary to find the dependence R th (p th ). Elektronika 11/2010
Using the measurement results for the considered transistor the following empirical dependence is proposed ⎡ ⎛ p ⎞ ⎛ ⎞⎤ = ⋅ ⎢ ⋅ ⎜ − th p + ⋅ ⎥ (6) ⎣ ⎜ − th R ⎟ ⎟ th Rth max a1 exp a2 exp ⎝ b1 ⎠ ⎝ b 2 ⎠ ⎦ where R thmax , a 1 , a 2 , b 1 and b 2 are the model parameters. In Table 2 the values of the parameters describing Eq. (6) for various cooling conditions of the investigated devices are collected. The investigations were carried out for the diode SDP10S30 and the transistor CRF24010F operating both without any heat-sink and situated on the small heat-sink. Measurements were performed with the electrical methods described in [14]. The results of the measurements – points and the calculations according to Eq. (6) – lines of the dependence of the diode and the transistor thermal resistance on the dissipated power are presented in Fig. 6. As seen, the measured and calculated results differ from each other not more than 5%, which confirms well the proposed model. In the presented figures, decreasing of the thermal resistance of both the investigated devices operating at the various cooling conditions on increasing of the device dissipated power is observed. It is also seen, that the dependence R th (p th ) is stronger for devices operating without any heat-sink. Z(t) [K/W] 35 30 25 20 15 10 5 SDP10S30 p th = 3.3 W p th = 4.7 W p th = 1 W p th = 2.1 W p th = 5.7 W 0 0,0001 0,001 0,01 0,1 1 10 100 1000 10000 t [s] Fig. 4. Measured (solid lines) and calculated (dotted lines) courses of Z(t) of the diode SDP10S30 Rys. 4. Zmierzone (linie ciągłe) i obliczone (linie kreskowe) przebiegi Z(t) diody SDP10S30 Z(t) [K/W] 100 80 60 40 20 CRF24010F T a = 20 o C p th = 0.51 W p th = 1.06 W p th = 1.5 W p th = 0.21 W p th = 2.03 W p th = 2.72 W 0 0,0001 0,001 0,01 0,1 1 10 100 1000 10000 t [s] Fig. 5. Measured (solid lines) and calculated (dotted lines) courses of Z(t) of the transistor CRF24010F Rys. 5. Zmierzone (linie ciągłe) i obliczone (linie kreskowe) przebiegi Z(t) tranzystora CRF24010F Tabl. 2. Values of the parameters in Eq. (6) for the diode SDP10S30 and the transistor CRF24010F Tab. 2. Wartości parametrów w równaniu (6) dla diody SDP10S30 i tranzystora CRF24010F a) Parameters Rth [K/W] b) Rth [K/W] Diode without any heat-sink Diode on the heat-sink Transistor without any heat-sink Transistor on the heat-sink R thmax 78 34 93 22.2 80 70 60 50 40 30 20 10 a 1 0.88 0.9 0.85 0.92 a 2 18 25 18 45 b 1 0.12 0.1 0.15 0.08 b 2 1.5 1.5 0.7 1.5 0 0 1 2 3 4 5 6 p th [W] Fig. 6. Calculated and measured dependences of the thermal resistance of the diode SDP10S30 (a) and the transistor CRF24010F (b) on the dissipated power Rys. 6. Obliczone i zmierzone zależności rezystancji termicznej diody SDP10S30 (a) oraz tranzystora CRF24010F (b) od mocy It probably results from the fact, that the influence of the heat conduction, radiation and convection is different in the devices situated on the heat-sink and operating without it. As it is seen, that in the considered range of device dissipated power the device thermal resistance can change even more than 20%. Conclusions SDP10S30 device without any heat-sink device on the heat-sink 100 90 CRF24010F 80 device without any heat-sink 70 60 50 40 30 20 device on the heat-sink 10 0 0 2 4 6 8 10 p th [W] In the paper the compact nonlinear thermal model of two SiC semiconductor devices is proposed. The accuracy of this model is verified on the example of the power MESFET transistor CRF24010F and the Schottky diode SDP10S30. A good agreement between the measurements and the calculations with the use of the new model in the wide range of changes of the device dissipated power and for various conditions of theirs cooling is achieved. Elektronika 11/2010 11
Page 3 and 4: ok LI nr 11/2010 • MATERIAŁY •
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