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RF Electronics Chapter 2: Computer Simulation Page 35 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. project file for figure 2.42 uses a pulse width TW=2.67 s and 32 harmonics for the harmonic balance simulation. That project file will not converge for >48 harmonics. When R L = 120 , high frequency oscillations occur in the transient response as shown in figure 2.40. As a result, the harmonic balance simulation fails to converge. For most RF circuits, square waves are not used, so that a high number of harmonics is not required to represent the waveforms accurately. As a result, convergence is normally achieved. The transient analysis fully includes all nonlinearities specified in the device parameters and accurately incorporates unexpected conditions like the oscillations shown in figure 2.40. Accurate nonlinear analysis as described here is thus essential in ensuring a design operates fully as required over all expected input and load conditions. The Transient and Harmonic Balance simulations give very similar steady state results, but for <32 harmonics, APLAC HB simulation is normally quicker. Black Box Matching of Circuits to Measurements Sometimes one needs to model an existing device, without having direct access to all the elements making up that circuit. An example [9,27] is the development of a model can be used to model a mains power distribution transformer, at frequencies up to 5 MHz, so that one knows the impedances the transformer presents at Power Line Carrier frequencies (up to 150 kHz), which are used for Smart Grid applications or determining the effects of lightning through power networks. A single-phase power distribution transformer has 2 terminals for its low voltage (LV) winding, 2 terminals for its medium voltage (MV) winding and a terminal for the metal case of the transformer, a total of 5 terminals. A 3- phase power distribution transformer has 3 LV phase terminals, 3 MV terminals, a Neutral terminal and a case, a total of 8 terminals. To simplify the model, each LV phase winding and each MV winding is assumed to be identical. So that a similar model to the single phase transformer results, as shown in [27]. One can measure the impedances seen between any 2 of the 5 terminals of a single phase transformer. As shown in [9], a sufficiently accurate model can be developed using 5 measurements, rather than the 10 possible measurements that can be made between the 5 terminals. The problem now becomes how to match the components in the model to those impedance measurements. One could write down equations for the impedances that can be seen in each of the 5 measurement points and solve the resulting complex equations to obtain the component values. Since the impedances of the inductances and capacitances change with frequency, solving these equations is an exceedingly difficult task. It is possible to guess a circuit configuration and use MWO and optimisation tools, to "solve" the simultaneous equations by optimisation and match the circuit elements to the measurements. To illustrate this technique, the process is performed on a relatively simple network. Example 2.5: Bandpass T Matching Network A simple Bandpass T matching network described in Chapter 9 "Impedance Matching of Power Amplifiers" of this book is used to illustrate the impedance matching process. These networks are used to match power transistors to 50 Ω loads. For this example, an input matching network is chosen to match a device with an input impedance of X D = 5 + j 0.9 Ω to a source with X L = 50 Ω at 150 MHz with a Q of 3.5. The equations in Chapter 9 are entered into the Global Definitions window, as shown in figure 2.43. Two versions of the circuit are shown in figures 2.44 and 2.45 respectively. Lbt, Cbt1 and Cbt2 are the RF Electronics: Design and Simulation 35 www.cadence.com/go/awr

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