# Alternative Categorization of Radio Frequency Power Amplifier for Generalized Design Insights
## 3 Alternative Categorization
### Time  
A thorough analysis of the term \(P_{diss}\), which is related to the time domain waveform of voltage and current, is presented in this subsection. It refers to the dissipated power loss at the RFPA due to the simultaneous presence of voltage and current at the same time. In this context, the active device of the RFPA will be referred to as a transistor, without any loss of generality. The period when the RFPA is active, meaning that both the current and voltage time domain waveforms exist simultaneously in the device, is measured using the conduction angle, \(\theta=\omega t\). This conduction angle, which is a function of time and angular frequency and is represented in degrees, is referred to as time in this work. Figure 2 presents the normalized voltage and current waveforms at the drain of the RFPA. In Figure 2a, the device conducts the entirety of a full cycle with a conduction angle of 360\({}^{\circ}\), leading to high-power dissipation. In contrast, in Figure 2b, the device only conducts for half the period. These variations in power dissipation through the time domain waveform drive the exploration of ways to optimize the RFPA's efficiency. By strategically imposing a non-overlapping condition, as given by Equation (5), precise control over the device's operation is achieved. \[\frac{1}{t_{o}}\int_{0}^{t_{o}}V_{ds}(t)\cdot I_{ds}(t)=0 \tag{5}\]  
By engineering the timing and duty cycle of the voltage and current waveforms on the transistor, the RFPA can be designed in such a way as to eliminate any wasteful power dissipation. In fact, within the field of RFPA design, more advanced classes of waveforms can be employed, as shown in Figure 3. Class E amplifiers, which are also known as switch-mode amplifiers, are one such example. They operate by rapidly switching between on and off states, reducing power dissipation. On the other hand, Class F amplifiers, known as current-mode amplifiers, focus on shaping the voltage waveform to enhance efficiency. These classes of waveforms employ techniques to ensure non-overlapping conditions between the current and voltage waveforms, aiming to achieve theoretical efficiencies of 100%. Figure 2: Time domain overlapping voltage and current waveforms. (**a**) Conduction angle of 360; (**b**) conduction angle of 180\({}^{\circ}\). Efficiency can be expressed in terms of the conduction angle \(\theta\), as shown in Equation (6), wherein \(\left(v_{f}\right)_{max}\) represents the maximum output voltage at the fundamental design frequency, and \(V_{DD}\) is the supplied voltage [19]. The theoretical efficiency achievable as a function of this conduction angle is shown Figure 4. Maximum efficiency can be achieved by choosing an appropriate design for the biasing and load networks, ensuring as little overlap as possible between the two waveforms during the operation of the RFPA. \[\eta=\frac{\theta-sin\theta cos\theta}{sin\theta-\theta cos\theta}\left(\frac {\left(v_{f}\right)_{max}}{V_{DD}}\right) \tag{6}\]  
These findings highlight how crucial it is to carefully consider voltage and current waveforms to achieve highly efficient RFPA. By implementing the non-overlapping condition and carefully engineering the waveforms, remarkable reductions in energy losses can be achieved, thereby enhancing the overall performance of the system. That is why RFPA design is often referred to as waveform engineering [21]. In general, the time domain voltage and current waveform can be approximated as Equations (7) and (8), respectively [22]. \[V_{ds}(\theta) \approx(1-\alpha cos\theta-\beta cos2\theta-\gamma cos3\theta)(1- \delta sin\theta) \tag{7}\] \[I_{ds}(\theta) \approx(1+wcos\theta+xcos2\theta+ycos3\theta)(1-zsin\theta) \tag{8}\]  
The parameters \(\alpha\) = [1, \(\sqrt{2}\) or 2/\(\sqrt{3}\)], \(\beta\) = [0 or 1/2], \(\gamma\) = [0 or 1/(3\(\sqrt{3}\))], and \(\delta\) = [\(-\)1 to 1] define their time domain voltage waveforms.