A Conjugate Numerical-RC Network Prediction of the Transient Thermal Response of a Power Amplifier Module in Handheld Telecommunication

Abstract

A study compares two different approaches (numerical vs. RC Network) used to predict the transient thermal response of a Radio Frequency (RF) Power Amplifier (PA) module at a given duty cycle (power on and off periodically) in handheld telecommunication. In the numerical approach, commercial software is used to predict device’s transient thermal response at any arbitrary time of interest for a given set of material properties. To predict the peak and valley temperatures of the device when it reaches steady state, a new methodology is presented, combining the steady state temperature at an averaged power and the temperature difference between single-pulse (at averaged power) and a periodical curve at peak or valley. For multiple heat sources, a linear superposition theory applies. Temperature at any given junction and at any specific time, is a linear superposition of its response to the power applied at all junctions (including itself) summed up over all preceding time history. In the analytical Resistor-Capacitor (RC) network approach, the R’s (thermal resistances) and τ’s (time constants) in a single-pulse are predicted using linear regression curve fitting techniques. For a single-pulse RC model, superposition methodology is applied to solve the transient response in any waveform (single or multiple waves in a cycle). A formulated spreadsheet performs the calculation, with inputs such as pulse width, waiting time (before the pulse is initiated), pulse magnitude and period. The peak and valley temperatures at steady state for a single square wave per cycle are predicted through closed form solutions. For multiple square waves per cycle, individual wave responses must be added together throughout the entire range of the steady state cycle to determine the locations (time) of the peaks and valleys. In order to compare these two approaches, two case studies were conducted on a PA module for a cell phone application: at 12.5% duty cycle and at three-square wave per cycle. Results show good agreement between the numerical and RC model approaches, either at any arbitrary time or at “peak and valley” in steady state. Although the RC network method requires an intermediate creation of the RC model from single pulse numerical solutions (or from experimental measurement), the total time and effort to achieve similar results as compared to the direct numerical method may be considerably reduced. Further, once created, the RC model permits essentially unlimited flexibility and extremely rapid computation for arbitrary power cycling, whereas the direct numerical approach requires “starting over” with every different power cycling description of interest.