Active Components

Continuous Class-F

Q: How does continuous Class-F differ from standard Class-F?

Standard Class-F enforces a single ideal condition: a short circuit at every even harmonic and an open circuit at every odd harmonic, which flattens the drain voltage and half-rectifies the current to reach a theoretical 90.7 percent efficiency with the third harmonic controlled. Continuous Class-F keeps the same fundamental and second-harmonic current/voltage shaping but multiplies the voltage waveform by a (1 minus gamma times sin theta) reactive factor parameterized by gamma, typically swept from minus 1 to plus 1. Each value of gamma is a valid, fully efficient solution, so instead of one impedance target you have a continuum of fundamental and harmonic impedances. Because those targets trace arcs on the Smith chart rather than single points, a matching network can satisfy the efficiency condition across a 40 to 60 percent fractional bandwidth instead of the narrow band a fixed-point design allows.

Q: What harmonic impedances does a continuous Class-F design require?

At the fundamental the optimum load presents R_opt in series with a reactance that moves with gamma, so the fundamental target sweeps an arc around the resistive Class-F point. The second harmonic must be terminated in a pure reactance whose value also tracks gamma; it is no longer a hard short but a controlled reactive termination, X2 proportional to gamma. The third harmonic is ideally held at an open (high impedance) just as in conventional Class-F, since the odd-harmonic peaking is what flattens the voltage. In practice designers control the fundamental, second, and third harmonics and let the fourth and higher fall where the device output capacitance places them. The key relaxation is that the second-harmonic reactance is allowed to be non-zero, which is exactly what frees the design to cover a wide band.

Q: Why does continuous Class-F give wider bandwidth than Class-F?

In a fixed Class-F design the matching network must hit an exact resistive fundamental, an exact second-harmonic short, and an exact third-harmonic open at one frequency. Those single points are physically impossible to maintain over frequency because a real matching network and the device output capacitance rotate the impedance with frequency. Continuous Class-F replaces each single point with a locus: as frequency changes and the network naturally rotates the presented impedance, the design simply lands on a different but equally valid gamma solution. Reported GaN HEMT realizations cover roughly 1.5 to 2.5 GHz or 1.6 to 2.7 GHz at 70 to 75 percent drain efficiency and 10 to 13 W, where a classical Class-F device would hold high efficiency over only a few percent bandwidth.

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Generalizing the ideal Class-F amplifier conditions into a continuous family of solutions, this design mode replaces the single fixed harmonic short and open with a one-parameter set of reactive fundamental and harmonic terminations indexed by γ (typically −1 to +1). Every value of γ preserves the squared drain voltage and high drain efficiency, so the optimum impedances become arcs on the Smith chart rather than single points. That freedom lets a broadband matching network and the device output capacitance track a valid solution across frequency, yielding GaN HEMT power amplifiers that hold 70 to 75% drain efficiency over 40 to 60% fractional bandwidth instead of the few-percent band a classical Class-F design allows.

Category: Active Components

Drain Efficiency: 70 to 75%

Fractional BW: 40 to 60%

The Continuous-Mode Solution Space

Conventional Class-F operation rests on one rigid recipe: terminate every even harmonic in a short and every odd harmonic in an open. The resulting flattened voltage waveform and half-sinusoidal current barely overlap, which is why the ideal mode reaches 90.7% efficiency when only the third harmonic is controlled (the maximally flat two-harmonic voltage solution) and approaches 100% as more odd harmonics are added. The problem is that those impedance conditions are single points at a single frequency, and no physical matching network can hold an exact short and an exact open across more than a sliver of bandwidth. Continuous Class-F, introduced by Carrubba, Cripps, and colleagues, dissolves that constraint by recognizing that the Class-F voltage waveform can be multiplied by a reactive shaping factor without raising any negative voltage excursion.

The shaping factor is (1 − γ sinθ), where θ is the normalized phase of the fundamental drive and γ is the continuous design parameter. At γ = 0 the waveform collapses to the textbook maximally flat Class-F drain voltage (a true square wave only in the limit of infinite odd harmonics). As γ sweeps from −1 to +1, the fundamental load picks up a reactive part and the second-harmonic termination moves off the short into a controlled reactance, while the third harmonic stays near an open. Each γ is a complete, fully efficient amplifier in its own right, so the designer is no longer hitting three points but riding a continuous locus of targets.

Because impedance naturally rotates with frequency through the package, bond wires, and output capacitance of a GaN HEMT, a continuous Class-F network can be engineered so the presented impedance lands on a different but equally valid γ at each frequency in the band. That is the mechanism behind reported designs spanning roughly 1.5 to 2.7 GHz at better than 70% efficiency, performance that is verified on the bench with load-pull characterization to confirm the harmonic arcs.

Governing Waveform Relations

Continuous Class-F voltage waveform:
v_DS(θ) = (1 − α cosθ + β cos3θ)(1 − γ sinθ)

Optimum harmonic terminations vs. γ:
Z₁ ≈ R_opt(1 + jγ)   (fundamental, reactive arc ∝ γ)
X₂ ∝ γ · R_opt   (2nd harmonic, pure reactance, sign tracks γ)
Z₃ → ∞   (3rd harmonic, open)

Ideal drain efficiency (3rd-harmonic peaking):
η_max = π√3/6 ≈ 90.7% (ideal, γ-independent) → lower with finite knee

Where α ≈ 2/√3 and β ≈ 1/(3√3) set the maximally flat voltage, R_opt ≈ (4/√3)(V_DD − V_knee)/I_max for the maximally flat case, and γ spans −1 to +1. Each γ holds the same η while shifting Z₁ and X₂.

Mode Comparison for High-Efficiency PAs

Mode	Ideal Drain Eff.	2nd Harmonic	3rd Harmonic	Typical Frac. BW	Notes
Continuous Class-F	90.7% (3rd)	Reactive arc (∝γ)	Open	40 to 60%	Broadband, design locus
Class-F	90.7% (3rd)	Short	Open	2 to 8%	Narrowband, fixed points
Inverse Class-F	90.7% (3rd)	Open	Short	2 to 8%	Swaps current/voltage shaping
Class-J	~78.5%	Reactive (∝β)	Soft	30 to 50%	Wideband, no 3rd-harmonic open
Class-E	~85 to 90%	Capacitive	Switch-defined	5 to 15%	Switch-mode, high peak voltage

Common Questions

Frequently Asked Questions

How does continuous Class-F differ from standard Class-F?

Standard Class-F fixes a short at every even harmonic and an open at every odd harmonic, giving one impedance target and 90.7% ideal efficiency with third-harmonic control. Continuous Class-F multiplies the voltage waveform by a (1 − γ sinθ) reactive factor, with γ swept from −1 to +1. Every γ is fully efficient, so the fundamental and second-harmonic targets become arcs on the Smith chart instead of points, and a matching network can satisfy the condition over a 40 to 60% band.

What harmonic impedances does a continuous Class-F design require?

The fundamental presents R_opt plus a γ-dependent reactance, sweeping an arc around the resistive Class-F point. The second harmonic is a controlled reactance X₂ ∝ γ rather than a hard short. The third harmonic is held near an open to flatten the voltage. Designers typically control the first three harmonics and let the fourth and higher settle where the device output capacitance places them; allowing a non-zero second-harmonic reactance is what opens the band.

Why does continuous Class-F give wider bandwidth than Class-F?

Fixed Class-F must hit an exact resistive fundamental, a second-harmonic short, and a third-harmonic open at one frequency, which a real network and the device capacitance cannot hold across frequency. Continuous Class-F replaces each point with a locus, so as the network rotates impedance with frequency the design lands on a different valid γ. GaN HEMT realizations report 1.5 to 2.7 GHz coverage at 70 to 75% drain efficiency and 10 to 13 W.

Related Terms

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