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RFIC PA Development for Communication and Radar Systems

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RFIC PA Development for Communication and Radar Systems 5 Power amplifiers generally operate with narrowband signals in the form of modulated carriers, which are characterized as having a periodic high-frequency carrier signal and a low-frequency modulation signal that act on either the amplitude, phase, or frequency of the carrier. The ratio between the lowest frequency present in the modulation and the frequency of the carrier is a measure of the relative frequency resolution required of the simulation. General-purpose circuit simulators, such as SPICE, use transient analysis to predict the nonlinear behavior of an amplifier. Transient analysis is inefficient when it is necessary to resolve low-modulation frequencies in the presence of a high-carrier frequency because the high-frequency carrier forces a small time step while a low-frequency modulation forces a long simulation interval. In addition, most SPICE simulators lack accurate and effective modeling solutions for the distributed components so common in high frequency design. In contrast, HB simulation is a fast and effective means for accurately predicting the steady-state performance of RF, microwave, and mmWave circuits. The extensive substrate specific and EM-derived passive models used in RF/microwave circuits are typically described in the frequency domain. Achieving equivalent behavior for these models when used in time-domain SPICE simulations is challenging, requiring excessively long simulation run times. One limitation of traditional HB analysis occurs when it is used to solve large circuits with many different signal tones because it requires long computational times and large amounts of computer memory. To make HB viable when analyzing such circuits, Cadence design software developers have developed a multi-rate harmonic balance (MRHB) technology within its AWR APLAC ® family of HB and time-domain simulators. MRHB overcomes the aforementioned limitations, significantly reducing the solution time as well as the computer memory required when applied to frequency-rich nonlinear systems that have multiple signal tones. The capabilities provided with MRHB make it possible to solve entire complex subsystems such as mobile phone transceivers in a practical amount of time. A single-tone HB analysis simulates the circuit at a fundamental frequency, at integer multiples of the fundamental frequency, and at DC. Single-tone HB analysis requires the specification of a fundamental frequency (or a frequency sweep) and the total number of harmonics. HB also supports multi-tone analysis. While harmonic distortion is often used to describe nonlinearities of analog circuits, certain cases required other measures of nonlinear behavior. For example, suppose the nonlinearity of a narrowband PA is to be evaluated. The narrow band causes its harmonics to fall out of the passband, and then the output distortion appears quite small even if the PA introduces substantial nonlinearity. Intermodulation distortion (IMD) based on two-tone simulations/measurements is commonly used to characterize in-band spurious tones generated by amplifier nonlinearities. As shown in Figure 6, when two signals with different frequencies are applied to a nonlinear system, the output in general exhibits some components that are not harmonics of the input frequencies and are called intermodulation (IM). This phenomenon arises from "mixing" (multiplication) of the two signals when their sum is raised to a power greater than unity. Figure 6: IM products resulting from two-tone excitation of a nonlinear network

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