Figure 6.11: Plots of output power, PAE, and power gain versus Pin, respectively.
In this section, we demonstrate some single-tone and two-tone character-istics, which extracted from the time-domain simulation of a three-finger HBT device. For the finger of this device, not only self-heating effect of itself has been considered, but also the heat coupling from other fingers is counted. The related algorithm is discussed in Sec. 3.1.4. We note that the parameters of this device is listed in Table 4.2, and the theoretical values of thermal resistances RT H0, RT C1 and RT C2 are 1834.20, 487.04 and 101.43 ◦C/W, respectively.
As the input excitation is a single-tone signal at 1.8 GHz, Fig. 6.11 shows the output power (POUT), power-added efficiency (PAE), and power gain for different values of input power (Pin). The definition of PAE is written as:
PAE ≡ Output Power − Input Power
DC Dissipated Power ≈ POUT− Pin
IC,DC· VCC. (6.2) The bias condition of this single-tone simulation is with VCC = 3.6 V and
Pin (dBm)
-22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0
PAE (%)
0 20 40 60 80 100
Finger 1 Finger 2
Figure 6.12: Plots of PAE for Finger 1 and 2 versus Pin.
IIN = 0.6 mA. In this simulation, we have taken the heating effect of input RF power into consideration by adjusting average power for junction temper-ature iteratively. It is found that, shown in Fig. 6.11, the power gain and PAE
degrade as Pin increases. With the curve of power gain, we can find the input power where the power gain decrease for 1-dB in magnitude. This input power is called 1-dB compression point (P1dB) and it equals −2.45 dBm in this case.
The thermal coupling effect among fingers also influenced the performance of the three-finger device. As shown in Fig. 6.12, the PAE of the central finger (Finger 2) is lower and degrades when Pin > −3 dBm. In the meanwhile, the PAE of side finger (Finger 1) still raises as Pin increases. This phenomenon illustrates that the performance degradation of the whole transistor is mainly caused by the hotter central finger.
IIN (A)
4.0e-4 6.0e-4 8.0e-4 1.0e-3 1.2e-3
JCC (kA/cm^2)
Figure 6.13: Plots of the collector current density (JCC) versus the input bias current (IIN) for the cases A, B, C, and D.
For two-tone intermodulation simulation, we perform four testing cases in this section. Each case uses the same model parameters (as shown in Ta-ble 4.2), VCC bias (3.6 V) and a two-tone excitation input. The input power of each tone is −10 dBm and the frequencies of this two-tone signal are 1.71 and 1.89 GHz, respectively. In the case A, we ignore all thermal effects, in other words, RT H0 = RT C1 = RT C2 = 0 ◦C/W. Only the self-heating effect is included in the caseB, which means RT C1 = RT C2 = 0◦C/W and RT H0 = 1834.20◦C/W. For the caseC, we consider both the self-heating and
IIN (A)
4.0e-4 6.0e-4 8.0e-4 1.0e-3 1.2e-3
T J (K)
Figure 6.14: Plots of the junction temperature (TJ) versus IIN
for the casesB, C, and D.
thermal coupling effects, and the values of thermal resistances RT H0, RT C1
and RT C2 are 1834.20, 487.04 and 101.43 ◦C/W, respectively. Finally, the case D has the same conditions as the case C, besides the consideration for heating effect of input RF signal. To incorporate the heating from the input signal for the caseD, the averaged additional power is iteratively calculated with Eq. (4.2) and Eq. (4.3) until the junction temperature TJconverged.
The collector current density (JCC) and junction temperature (TJ) of each finger in all cases are shown in Fig. 6.13 and Fig. 6.14, respectively. In the caseA, TJkeeps a constant value (300 K) and JCC rises almost linearly as IIN
increases since the thermal effects are ignored. It is found that, in the case B, there are suddenly jump for JCC and TJ when IIN > 0.9 mA. Furthermore, both JCC and TJ of Finger 2 are higher than those of Finger 1 in the casesC andD. Because of the consideration for additional heating from the RF input signal, TJin the caseD is higher than that in the case C, and JCCin the caseD is contrastively lower.
IIN (A)
2.0e-4 4.0e-4 6.0e-4 8.0e-4 1.0e-3 1.2e-3
OIP3 Value (dBm)
23 24 25
26 Case A
Case B
Figure 6.15: A comparison of OIP3 values under different biases IINbetween the casesA and B.
Figure 6.15 shows the plots of OIP3 values versus IINfor the testing cases A and B. OIP3 values of the case A are higher than those of the case B for the neglect of thermal effects in the caseA. As IIN> 0.9 mA, the OIP3 value
IIN (A)
4.0e-4 6.0e-4 8.0e-4 1.0e-3 1.2e-3
OIP3 Value (dBm)
26.4 26.6 26.8 27.0 27.2 27.4
Case C Case D
Figure 6.16: A comparison of OIP3 values of the whole device under different biases IINbetween the casesC and D.
begins to drop, and JCC and TJ rise abruptly in the meantime, as shown in Fig. 6.13 and Fig. 6.14. The self-heating effect downgrades the two-tone lin-earity of HBT in the caseB. We take the thermal coupling effect among fingers into account in the casesC and D. It is found that, as shown in Fig. 6.16, OIP3 value of the whole device varies smoothly with IIN. Because there are two cold fingers (Fingers 1 and 3) in the cases C and D, the abrupt degradation for linearity in the caseB can be prevented. In comparison between the cases C and D, OIP3 values in the case D are slightly lower than those in the case C for additional heating induced by the input RF signal. Furthermore, we
IIN (A)
4.0e-4 5.0e-4 6.0e-4 7.0e-4 8.0e-4 9.0e-4 1.0e-3 1.1e-3 1.2e-3
IIP3 Value (dBm)
0 1 2 3 4 5
Finger 1 of case C Finger 2 of case C Finger 1 of case D Finger 2 of case D
Figure 6.17: Plots of the input third-order intercept point (IIP3) values versus IINof the caseC and D.
demonstrate the input third-order intercept point (IIP3) values for each finger in Fig. 6.17. It is reasonable that the colder finger (Finger 1) has better lin-earity. In comparison with the caseC, the difference in linearity performance between fingers for the caseD is enlarged by the additional heating. This ex-pansion of difference among fingers lowers the OIP3 values of whole device as shown in Fig. 6.16.
6.4 Summary of This Chapter
We demonstrated several two-tone intermodulation and power characteristics of HBTs in this chapter. From the comparison of OIP3 values between our time-domain and ADS harmonic balance solver, our developed kernel shows its capability to solve the steady-state circuit problem, which is not suitable for traditional time-domain circuit solver. Besides, as we introduce the ther-mal effects into the circuit simulation, the influence of device heating both on power and linearity performance has been simulated by our simulator. The itemized list of the contents in this chapter is shown as:
• the comparison between our and HSPICE time-domain solver in solving OIP3 values,
• the two-tone intermodulation distortion analysis computed by both our and ADS solver,
• the intermodulation distortion characteristic of an HBT as the self-heating been counted, and
• power and two-tone linearity characteristics of an multi-finger HBT with the consideration of thermal coupling effect.
Summary and Suggestions
T
o solve the nonlinear circuits, which include active semiconductor de-vices, a time-domain solution technique based on the WR, MI, and RK methods has been successfully developed in this dissertation. With the MI technique, we have numerically demonstrated each decoupled circuit ODE converges monotonically in Chapter 3 and Appendix C. Compared with com-mercial simulators, such as HSPICE and ADS, our solution method has been presented to show its accuracy and efficiency when evaluated against the mea-surement data. The proposed method here is not only an alternative computa-tional technique for the time-domain solution of circuit ODEs, but also can be generalized for high frequency circuit simulation including more and variant kinds of semiconductor transistors.In this chapter, we briefly summarize the essentials of our work first. Then, in the last section, some suggestions are proposed to further improve our study
130
and give the goals of future work.
7.1 Summary
We have stated the following key points in this dissertation:
• Chapter 1: the overview of this dissertation,
• Chapter 2: the mathematical models, which include the GP model equations for an HBT and the nodal equations of the tested circuits,
• Chapter 3: computational techniques, characterization methodology and measurement procedure,
• Chapter 4: DC simulation and analysis of the HBTs,
• Chapter 5: the results of time-domain simulation and frequency do-main analysis, and
• Chapter 6: the discussion of the intermodulation distortion and power characteristics.
In addition, we also present the appendices to complete the related issues of this dissertation.
• Appendix A: the equations of the MOSFET EKV model,
• Appendix B: the related EKV model simulation results,and
• Appendix C: the convergence properties of our developed numerical methods.
The major contribution of this work is the development of the transient analysis solver for high-frequency nonlinear circuit problems. The CAD pro-totype based on MI and Runge-Kutta methods has been applied to solving dif-ferent kinds of semiconductor compact models. The simulation results shows the advantages of the developed solver in comparison between HSPICE, es-pecially for the nonlinear circuits. We should emphasize that the proposed method only works when the KCL is valid. In other words, the limitation of the developed method is the operation frequency. Once the wave length of sig-nal competes with the device size, the electromagnetic effects should be took into consideration. Otherwise, the results of simulation becomes physically meaningless.