A Comparative Performance Analysis of Zero Voltage Switching Class E and Selected Enhanced Class E Inverters

This paper presents a comparative analysis of the class E and selected enhanced class E inverters, namely, the second and third harmonic group of class EFn, E/Fn and the class E Flat Top inverter. The inverters are designed under identical specifications and evaluated against the variation of switching frequency (f), duty ratio (D), capacitance ratio (k), and the load resistance (RL). To offer a comparative understanding, the performance parameters, namely, the power output capability, efficiency, peak switch voltage and current, peak resonant capacitor voltages, and the peak current in the lumped network, are determined quantitatively. It is found that the class EF2 and E/F3 inverters, in general, have higher efficiency and comparable power output capability with respect to the class E inverter. More specifically, the class EF2 (parallel LC and in series to the load network) and E/F3 (parallel LC and in series to the load network) maintain 90% efficiency compared to 80% for class E inverter at the optimum operating condition. Furthermore, the peak switch voltage and current in these inverters are on average 20–30% lower than the class E and other versions for k > 1. The analysis also shows that the class EF2 and E/F3 inverters should be operated in the stretch of 1 < k < 5 and D = 0.3–0.6 at the optimum load to sustain the high-performance standard.


Introduction
The class E inverter has found numerous applications in radio transmission, induction heating, industrial ultrasonic, renewable energy systems, or the commercial electronics industry [1][2][3][4][5][6][7][8][9][10][11]. The widespread adoption of this inverter is mainly due to the compact structure with low component count and high-power driving capability. On top of that, if coupled with the zero-voltage switching (ZVS) or zero derivative voltage switching (ZVDS) techniques, it can operate with high efficiency even at very high switching frequency. The analytical modeling and design of the ZVS/ZVDS class E inverters are well reported in the literature [1,2,[8][9][10][11][12][13][14]. However, the class E has one big disadvantage. The high peak switch voltage (3.5 to 5 times depending simultaneously on the duty ratio, input inductance, and switching frequency) is of significant concern [15]. Henceforth, among other reasons, including improved stability and voltage regulation, the enhanced class E configurations are proposed to counter this issue. These inverters are classified as EF n or E/F n inverters where n defines the harmonic tuning component and realized by adding

The Circuit Configurations
The generalized class E and enhanced class E inverter topology is shown in Figure 1. The inductance L s and the capacitance C s resonate at a resonant frequency (f r ) according to a chosen quality factor (Q). The input inductance (L f ) is designed to provide a constant dc current, a very low ripple current. The input current ripple is inversely proportional to L f . The input capacitance C in facilitates the ZVS and absorbs the drain to source non-linear capacitance (C ds ) of the switch. The auxiliary resonant branch in EF n and E/F n inverters consists of the auxiliary resonant inductance (L 1 ) and capacitance (C 1 ) arranged in a series or parallel formation. They resonate at a frequency of nf s where f s is the optimum switching frequency and chosen to be greater than f r . The multiplier n is an integer and determined by L 1 , C 1 , and f s . The switch S 1 is operated at an optimum duty ratio D opt to achieve the ZVS operation. The switching pattern is given as follows.

Switch =
Turned ON, 0 ≤ θ < 2πD Turned OFF, 2πD ≤ θ < 2π Depending on the auxiliary resonant branch configuration, the EF n and E/F n inverters can be classified as demonstrated in Table 1. This classification is accompanied by a convenient 'short-form' representation. Throughout this document, these short-forms are used to refer to the corresponding inverter. The class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters are also known as 'second harmonic' and 'third harmonic' class E inverters, respectively.

Modes of Operation and Input Impedance (Z in )
In Figure 2, the impedance distribution and the currents are shown. The class E and class E based inverters operate in two modes. In mode 1, the switch S 1 is turned ON and the voltage across the capacitor C in falls to zero. The input current (I in ) flows through the switch S 1 and the L f stores energy. In the resonant tank, resonant current flows through the switch exchanging stored energy from C s to L s and completing half of the resonance cycle. By the end of this cycle, this current decreases, and the energy transfer is completed. In mode 2 as soon as S 1 is closed at θ = 2πD, I in diverts to charge the input capacitor C in , which eventually reaches the peak voltage before it discharges through the resonant tank. The peak voltage can also be signified as the peak switch voltage (V S1,peak ) of the inverter. Due to the inductive nature of the load network, the output current (I out ) lags the input voltage to the resonant tank (V S1 ). To achieve ZVS or ZVDS, the following conditions must be satisfied.
V S1 (2π) = 0 and d dθ V S1 (2π) = 0 The class E inverter demonstrates two resonant frequencies: f r1 (S 1 is ON) and f r2 (S 1 is OFF). These frequencies can be determined as follows.
Additionally, the quality factor (Q) of the circuit is defined as: Throughout this document, wherever f r is mentioned, it is meant to be the series resonant frequency f r1 . The input impedance of the resonant tank at the switch ON and OFF states are stated in Equations (1) and (2), respectively. (2) The class EF n and E/F n inverters incorporate an auxiliary resonant branch tuned to multiple n of the optimum switching frequency f s . The primary series resonant frequency is identical to that of class E and determined by the resonant inductance L s and resonant capacitance C s . The secondary resonant frequency f r2 in the class E and EF n (sLCpLN) can be characterized by parallel resonance and determined by the primary and auxiliary resonant components (L 1 , C 1 ) and their configurations. The input impedances for sLCpLN and pLCsLN configurations are stated in Equations (3) and (4) respectively. A representative diagram in Figure 2 shows the impedances and currents in the primary and auxiliary resonant networks. The primary and nth harmonic current is defined by i prires and i auxres , respectively. The definitions for variables A, B, C, D, and E are stated in Equations (10)- (14).
To exemplify the behavior pattern, the impedances are plotted in Figure 3 against ω for mode 2 according to the specifications described in Table 2. The primary series resonant frequency f r1 and the second parallel resonant frequency f r2 are identical for class E, EF 2 (sLCpLN), and E/F 3 (sLCpLN) configurations. This is shown in Figure 3a,b where ω fr1 /ω s ≈ 0.85 and ω fr2 /ω s ≈ 1. However, due to the series configuration of the L 1 C 1 to the load network, the primary resonance frequency (f r1 ) is altered in EF 2 (pLCsLN) and E/F 2 (pLCsLN) configurations. This is shown in Figure 3c, where ω fr1 /ω s ≈ 2 and ω fr1 /ω s ≈ 3 for EF 2 and E/F 3 , respectively. In addition to that, a third series resonance close to ω/ω s ≈ 1 (i.e., at f r3 ) occurs in EF 2 (sLCpLN) and E/F 3 (sLCpLN) configurations. This can be observed in Figure 3b, where ω fr3 /ω s ≈ 2 and ω fr3 /ω s ≈ 3 for EF 2 and E/F 3 , respectively. This feature, particularly, enables these inverters to transfer more power at identical input voltage (V in ), duty ratio (D), and switching frequency (f ) compared to class E. Additionally, a lower impedance for class EF n and E/F n , in general, induces lower loss and higher efficiency. A fourth parallel resonance can be found for both class EF 2 (sLCpLN, pLCsLN) and E/F 3 (sLCpLN, pLCsLN) inverters at much higher frequency, where ω fr4 /ω s > 4. Again, f r4 is characterized by parallel resonance and largely determined by the auxiliary branch components. . Input impedance (Z in ) of (a) class E at switch ON and OFF conditions (b) class EF 2 and EF 3 at switch OFF condition (c) class E/F 2 and E/F 3 at switch OFF condition at V in = 50 V, D opt = 0.5, f s = 220 kHz, R L = R L,opt , k ≈ 0.30 (EF 2 ) and 0.67 (E/F 3 ). 2.3. The Peak Switch Voltage (V S1,peak ) The capacitor current (i Cin ) in class E inverter can be expressed in terms of the input current (I in ) and the sinusoidal resonant current as: where, I m is the maximum resonant current. By integrating Equation (5) and applying the ZVS conditions [1,2], the switch voltage (V S1 ) and the peak switch voltage (V S1,peak ) can be derived as: where symbols carry their usual meaning. As can be noted, V S1,peak is a function of duty cycle (D), switching frequency (f ), and input capacitance (C in ). As for class E FT , V S1,peak can be approximated using Equation (9).
i Cin (ωt) = I in + I n sin(nωt) + I m sin(ωt + ϕ) V S1 = −2I in nπD + I in θn + nI m cos(2πD + ϕ) − nI m cos(θ + ϕ) + I n cos(2nπD) − I n cos(nD) ωnC in (9) As opposed to class E and E FT , i Cin and V S1,peak in class EF n and E/F n inverters are also a function of n [9,15]. The expression for i Cin and V S1 are shown in Equations (8) and (9), respectively. From Equation (9), V S1,peak is solved numerically and plotted in Figure 4 against ω, D, and C in at the optimum operating condition described in Table 2. In general, it decreases with increasing f and D. Additionally, at any given f and D, V S1,peak decreases with increasing C in . It is also to be noted that V S1,peak for the given case (i.e., k < 1) is higher for EF 2 inverters than class E and EF 3 counterparts. Furthermore, as the odd (particularly, 3rd) harmonic currents are emphasized (second harmonic being bypassed through the auxiliary branch), EF 2 switch voltage peak would have a flattening effect. This is observable in a later section (see Figure 5c).

Design of the Class E and Enhanced Class E Inverters
In this section, based on the analytical models described elsewhere [1,2,9,15,19,[25][26][27], the class E and enhanced class E inverters are designed. The inverters are designed to fulfill an identical requirement, specified in Table 2, to help formulate a fair comparison. The inverters share a common 'base' structure of class E with identical input inductance (L f ), resonant components (L s and C s ), and input capacitance (C in ) [2,28]. In this process, the following assumptions are involved:

•
All the components are ideal and do not possess any parasitic resistance, inductance, or capacitances.

•
The switch is ideal. The switch on-resistance is zero and off-resistance is infinite. The switching time is negligible.

Class EF n and E/F n Class E and E FT
Step 1 Choose V in , R L , and P out Choose V in and P out Step 2 Choose Q, n, and k Calculate R L,opt Step 3 Calculate D Choose n and D Step 4 Select f s Calculate phase shift, ϕ Step 5 Calculate C in Find input capacitance, C in Step 6 Calculate L 1 and C 1 Compute L f Step 7 Calculate L x Choose f r1 and Q Step 8 Calculate C s Choose f s > f r1 Step 9 Calculate L (L s + L x ) Calculate L s , C s Step 10 Calculate R DC C ex selected for desired V S1,peak and I S1,peak Step 11 Compute L f L is selected to maintain a switch flat top voltage

The Optimum Load Resistance (R L,opt )
Class E To start with the design process, the optimum load resistance for class E has to be determined for the rated output power P out . Hence, in a transformer less configuration, the optimum load resistance (R i ) is defined as Now, replacing V in = 50 V and P out = 25 W in Equation (14) and considering the transformer ratio: n, The voltage (V pri ) at the primary side of the transformer is a function of V in and D as defined by the following: where ϕ = phase of the resonant tank current and is defined as Now, replacing D = D opt in Equation (18): Replacing V in in Equation (17), we obtain: However, considering the specified output voltage V out = 5 V, the required transformer ratio is: Accordingly, R L,opt has to be updated as: The load resistance R L,opt for EF 2 (sLCpLN), EF 3 (sLCpLN), E/F 2 (pLCsLN), and E/F 3 (pLCsLN) is [11,28] selected as 4, 10, 3, and 2 Ω, respectively, to provide specified V out , P out and ZVS by varying switching frequency (f ).

The Optimum Duty Ratio
The optimum duty ratio for class E and EF FT inverter is 0.50 [2,19,25,26]. The optimum duty ratio for class EF n and E/F n inverters (n = 2) can be calculated from Equation (23) as ≈0.40. If n = 3, the concept described in [28] is used to determine the optimum duty ratio.

Class E
The input capacitance (C in,opt ) of the converter is given by: Replacing parametric values in Equation (23) gives us: Using the design curves presented in [11], the C in for EF 3 (sLCpLN) and E/F 3 (pLCsLN) can be calculated using Equation (26) to achieve ZVS for any given R L . However, [28] gives us more freedom to select any convenient C in (and rather vary f ) to achieve the ZVS condition. The latter technique is followed in this paper.

The Input Inductor (L f )
The input inductance (L f ) of the converter is given by: Replacing parametric values in Equation (27) gives us:

The Resonant Inductance (L s )
The resonant inductance can be determined as follows: Replacing the parametric values in (29) and assuming Q L = 7 and replacing f s gives us: 3.6. The Resonant Capacitance (C s ) Using f s and L s as determined in Equation (30) gives us, Replacing the parametric values in Equation (31) gives us: The design of L s and C s are applicable for class E, E FT , EF n , and E/F n inverters [2,9,27].

The Auxiliary Resonant Inductance (L 1 ) and Capacitance (C 1 )
By choosing k in Equation (33), C 1 is determined. The auxiliary resonant inductance (L 1 ) is then calculated from Equation (34). Similarly, this design of L 1 and C 1 is applicable for class E, EF n , and E/F n inverters [2,9,19,27].
3.8. The Capacitance (C ex ) and the Shifting Inductance (L) The capacitance (C ex ) and L have to be selected to maintain a flat top switch voltage, as well as for desired peak switch voltage and current. From Equation (35) as in [3], C ex and L can be determined. Here, m is selected to maintain a flat top switch voltage [3]. Accordingly, C ex = 2.5 nF and L = 6 µH are selected.

Simulation and Experimental Analysis
As mentioned earlier, the inverters are designed to satisfy an identical criterion described in Table 1 for objective comparison. Based on the analytical models, the circuit components for the corresponding inverters are designed. Accordingly, the inverters are tested in LTspice simulation environment, and the prototypes are built to support and verify the simulation data. The list of components used to build and test the prototypes are demonstrated in Table 4. In the next section, the experimental results are presented. In Figure 5a-c, the switch voltage waveforms of class E and EF n and E/F n prototype inverters at the optimum operating point are shown. In Figures 6-10, the performance parameters measured against f, D, k, and R L are demonstrated. A comparison at the optimum operating point is presented in Figure 6.   (c) normalized peak switch voltage, V S1,peak /V in ; (d) normalized peak switch current, I S1,peak /I m ; (e) normalized peak auxiliary resonant capacitor voltage, V C1,peak /V in ; (f) normalized peak resonant capacitor voltage, V Cs,peak /V in ; (g) normalized peak auxiliary resonant current, I Lc,peak /I m .

Results and Discussion
The inverters were experimentally tested by varying the switching frequency (f ), duty cycle ratio (D), capacitance ratio (k), and the load resistance (R L ). The primary objective was to evaluate the voltage and current at different points of interest. These parameters would help define the component ratings, the size of the inverter, and relative complexity in control. Eventually, a qualitative comparison can be formulated. The results are accumulated in Figures 5-10. The voltage regulation is defined as follows: In addition, the efficiency is measured as follows: η = P out P in × 100 = V rms I rms V dc I dc × 100 (37) Table 5 demonstrates a comparative cost difference of the class E and enhanced class E inverters. As low power inverters, the components are small in size. Hence, the induced cost for a single inverter is low. However, in general, the cost of building enhanced class E inverters could be more than 20% than that of the class E inverter. In addition, the cost would increase nonlinearly with the power rating of the inverter. The resonant tank of the inverters is designed to resonate at f r with a predefined quality factor Q. By varying the switching frequency f, the inverter rms output voltage, output power, peak switch voltage and current, and peak voltage across the resonant capacitors are measured. It was observed that the optimum operability (i.e., ZVS) sustained at the vicinity or close proximity of the resonant frequency f r . The power output capability was maximum in this region. As f increased, the resonant tank, which behaves like a bandpass filter, blocked the higher harmonics. Resultantly, the power flow was curtailed. Because of the higher input impedance (Z in ), the efficiency also dropped. In general, the peak switch voltage (V S1,peak ) and the peak resonant capacitor voltage (V C1,peak ) dropped with increasing frequency. This is due to the capacitor current (i Cin ), which also reduces with increasing f. The lowest V C1,peak were recorded for the pLCsLN configurations for k < 1. However, as more current was being diverted through the switch (S 1 ) from the auxiliary networks, there was an apparent rise in the peak switch current (I S1,peak ) for sLCpLN configurations. These results are demonstrated in Figure 7a-h.
The optimum duty ratio (D opt ) of class E inverter was 0.50, while for class EF n and E/F n inverters, it was approximately 0.40. Any deviation from these values would incur higher switching losses in the respective inverter type due to the loss of soft switching operation. In Figure 8a-h, the inverters were evaluated by varying the duty ratio (D) while operating at the corresponding optimum load (R L,opt ) and f s . It was observed that at extreme D (≥0.7), the energy delivered to the resonant tank deteriorated due to longer switch ON time. The energy stored in the input inductor (L f ) increased with D but mostly diverted through the switch S 1 . Hence, the switch voltage and current increases gave rise to switch conduction losses. Subsequently, the efficiency, while remaining fairly constant, dropped at extreme D. The highest efficiency was recorded for class E and the pLCsLN configurations at around 80-90% in the proximity of D opt . The peak resonant capacitor voltages were relatively unaffected by D. The peak switch current (I S1,peak ) was significantly higher (2-3 times) for sLCpLN configurations at k < 1. However, this could be lowered significantly by operating the inverters at higher k (>1). This fact is demonstrated in Figure 8c. The peak auxiliary resonant current (I L1,peak ) in the sLCpLN configurations became significantly higher at extreme D however, this could be avoided by increasing k.
The ratio k is defined by the ratio of the input capacitance to the auxiliary resonant capacitance (C in /C 1 ). The variation k can be translated as the variation of the auxiliary resonant components (L 1 and C 1 ) while keeping n constant. Hence, by definition, increasing k means decreasing C 1 and increasing L 1 and vice versa. In general, with increasing k, the rms output voltage and power output capability (c p ) drops. The efficiency (η) also drops with higher k. This is shown in Figure 9a-h. k < 1, V S1,peak , and I S1,peak for sLCpLN configurations were significantly higher (2-3 times) than class E and pLCsLN configurations, as mentioned earlier. This was mainly due to the excessive energy that was stored in the large resonant capacitor C 1 and subsequently dissipated through the switch at the turn ON instant. As k increased, the resonant inductance L 1 became bigger and diverted almost a constant current through S 1 . Hence, V S1,peak and I S1,peak remained fairly constant at higher k. However, because of smaller C 1 at higher k, a relatively larger voltage was induced across C 1 (i.e., V C1,peak ).
On the other hand, the increasing load resistance (R L ) drove the inverter operating from continuous conduction mode (CCM) to the discontinuous conduction mode (DCM). Hence, V out,rms and c p decreased, with increasing R L being maximum at R L,opt . The peak switch voltage and current (V S1,peak and I S1,peak ) remained fairly constant over the entire load range. V C1,peak and I L1,peak were relatively higher (2-4 times) for sLCpLN configurations. The voltage regulation (VR) was higher at lower loads. The results are demonstrated in Figure 10.
In Figure 6, the performance parameters recorded at the optimum operating point (D opt = 0.50 or 0.40, R L = R L,opt ) are demonstrated. The maximum and minimum quantities are marked in 'red' and 'sky blue', respectively. As obvious from Figure 6a, c p is maximum for class E and EF 2 (sLCsLN) configuration at k > 1, recorded as 0.1356 and 0.215, respectively. The lowest is 0.01 for EF 2 (sLCsLN) configuration at k < 1. Again, as shown in Figure 6b, the class E and pLCsLN configurations demonstrated higher efficiency compared to the sLCpLNs. The maximum and minimum efficiency were recorded for class E/F 3 (pLCsLN) (k < 1) and E/F 3 (sLCpLN) (k < 1) as 91% and 58%, respectively. However, η did not vary largely with k. The peak switch voltage in Figure 6c was generally lower for higher k. The maximum and minimum are recorded for class EF 2 (sLCpLN) at 5.1 and 2.74 for k < 1 and k > 1, respectively. However, a further reduction of V S1,peak was possible by increasing k, as demonstrated in Figure 9c. The peak switch current (I S1,peak ) was generally higher in sLCpLN compared to the pLCsLN configurations. The highest and lowest I S1,peak were recorded at 3.25 and 1.17 for class EF 2 (sLCpLN) (k < 1) and class E, respectively, as demonstrated in Figure 6d. From Figure 9d, it can be deduced that selecting k > 1 and k < 1 for sLCpLN and pLCsLN can minimize I S1,peak further. The peak voltage across the resonant capacitor (V C1,peak ) was lower for pLCsLN configurations (2-3 times than sLCpLN in general), as can be observed in Figure 6f. This is expected as the voltage across the load network is shared across the capacitors Cs and C1 for pLCsLN configurations. On the other hand, the peak current in the auxiliary resonant network (I L1,peak ) is notably higher for k < 1 (See Figure 9g). The summary of these findings and optimum operating conditions for enhanced inverters are accumulated in Table 6. Table 6. Summary.

Efficiency (η)
1 Class EF n and E/F n inverters operate more efficiently at optimum load at: Efficiency wise, class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters outperform class E and others with maximum efficiency recorded as 86 and 94%, respectively, at the optimum operating point.
The power output capability (c p ) 1 The power output capability (high output power at lower switch stress) of class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters is on par with class E at the optimum load: Highest power output capability at the optimum operating point is recorded for class EF 3 (pLCsLN) as ≈0.10. The output voltage and power (V out and P out ) 1 The average output power of class E is higher than the class EF n and E/F n inverters across the switching frequency (f s ), duty cycle ratio (D), capacitance ratio (k), and the load resistance (R L ).

2
The output voltage and output power of class EF 2 (sLCpLN) are not severely affected by k.

Efficiency (η)
1 The peak switch voltage for class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters are 20-30% lower than class E, particularly: • at D = 0.2 − 0.7 for any load condition • for any k at the optimum load 2 The peak switch voltage of class EF 2 (sLCpLN) and E/F 3 (sLCpLN) are 40-50% higher than the other inverters at the optimum operating point. However, they are considerably higher, particularly: Comparatively, the peak switch voltage is not affected considerably by the load change.
The peak switch current (I S1,peak ) 1 The peak switch current for class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters is lower than class E for any D and load condition. 2 The peak switch current of class EF 2 (sLCpLN) is comparatively higher than class E and other variations of EF n and E/F n at the optimum load and: • for D > 0.65 and k < 1 The peak resonant capacitor voltage (V cs,peak ) 1 The peak resonant capacitor voltage is approximately 50% lower in class EF n and E/F n inverters than that in class E for any D, k and load condition The peak capacitor voltage (V C1,peak ) in the lumped network 1 The peak capacitor voltage in the auxiliary network is 2 to 5 times lower in class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters than in class EF 2 (sLCpLN).

2
The peak auxiliary resonant capacitor voltage of class EF 2 (sLCpLN) is, particularly, very high: The peak current (I L1,peak ) in the lumped network 1 The peak auxiliary resonant current in class EF n and E/F n inverters is on average 2-3 times higher for k < 1.
2 This current is particularly higher for class EF 2 (sLCpLN) inverter In addition to the comparison presented in Figures 7-10, the switching losses and THD are demonstrated in Figures 11 and 12 respectively. As can be observed, the switching loss is minimized due to application of ZVS and ZVDS. The percentage loss is maximum for class EF 2 (sLCpLN) at approximately 3.6%. The loss is minimum for class E/F 3 (pLCsLN) inverters at 3.08%. The THD can be greatly improved by adding extra filter at the output of the inverter.

Conclusions
In this paper, the class E and enhanced class E inverters are investigated for comparative performance analysis. Extensive simulation and experimental testing are performed in this regard. It is observed that the enhanced class E inverters excel beyond the conventional ZVS class E inverters in terms of efficiency and power output capability. This is also in line with the research published elsewhere. To be specific, the class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters demonstrate higher efficiency (8-10% higher) compared to other configurations. This is mainly due to the lowered switch conduction losses. In addition, the peak switch voltage and current are significantly lower (≈20-30%) in these inverters at the optimum operating condition while k > 1, and k = C in /C 1 . On the other hand, the peak capacitor voltages in all enhanced versions are lowered by 2-3 times on average. However, the peak current in the lumped auxiliary network of these inverters are 2-3 times higher. Based on the simulation and experimental results, it is recommended that class EF n and E/F n inverters are operated at 1 < k < 5 and D = 0.3-0.6 for sustained higher efficiency, power output capability, and lower switch stress.

Conflicts of Interest:
The authors declare no conflict of interest.

•
The average output power of class E is higher than the class EF n and E/F n inverters across the switching frequency (f s ), duty cycle ratio (D), capacitance ratio (k), and the load resistance (R L ).

•
The peak switch voltage for class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters are 20-30% lower than class E, particularly at D = 0.2 − 0.7 for any load condition and for any k at the optimum load.
• The average output power of class E is higher than the class EF n and E/F n inverters across the switching frequency (f s ), duty cycle ratio (D), capacitance ratio (k), and the load resistance (R L ).

•
The power output capability (high output power at lower switch stress) of class EF 2 (pLCsLN) and E/F 3 (pLCsLN) inverters are on par with class E at the optimum load for D = 0.4 − 0.7 and for k < 5.