Continuous Mode PA
Why Relaxing the Harmonic Condition Buys Bandwidth
The continuous modes grew out of a frustration with classic switching-mode amplifiers: they are gorgeous on paper and at one frequency, but their efficiency falls off a cliff the moment you move off the design point. A textbook Class-F amplifier needs the output network to present an open circuit at the odd harmonics and a short at the even harmonics so the drain voltage approaches a square wave and the current a half-sinusoid. Realizing that exact set of harmonic impedances over more than a few percent of bandwidth is essentially impossible, because passive networks cannot hold an open and a short at fixed multiples of a moving fundamental.
The breakthrough, formalized by Cripps, Carrubba, Tasker and colleagues around 2009 to 2011, was to notice that the maximally flat Class-F voltage waveform is only one member of a much larger family. Multiplying the waveform by a factor of (1 minus γ sinθ) leaves the peak voltage and the efficiency untouched but introduces a controllable reactive component into the harmonic terminations. The amplifier no longer demands a single magic impedance; it accepts any impedance that lies on the γ-locus. A broadband output network can then satisfy a different γ at every frequency in the band, which is what turns a single-point design into an octave-capable one.
Inverse continuous modes apply the same idea with the roles of voltage and current swapped, which suits devices and packages that prefer a capacitive output environment. In practice modern Class-F infrastructure PAs blend several continuous modes across the band, and the line between continuous Class-F, continuous inverse Class-F, and continuous Class-B/J becomes a smooth design continuum rather than a set of discrete classes.
Governing Waveform and Termination Equations
v(θ) = (1 − α cosθ + β cos3θ)(1 − γ sinθ)
with α ≈ 2/√3, β ≈ 1/(3√3), γ ∈ [−1, +1]
Fundamental and 2nd-harmonic load (normalized):
Z1 = Ropt(1 + jγ/2) Z2 = −j (3π/8) γ Ropt
Ideal efficiency (invariant in γ):
ηmax = π/(2√3) ≈ 90.7 %
Where θ = ωt, Ropt ≈ (VDD − Vknee) / Imax,fund is the optimum fundamental load, and Z3 is held near an open circuit. Sweeping γ rotates Z1 and walks Z2 around a reactive arc while η and peak voltage stay fixed.
Continuous-Mode Family Versus Discrete Classes
| Mode | 2nd-harmonic load | 3rd-harmonic load | Ideal efficiency | Realizable bandwidth | Typical use |
|---|---|---|---|---|---|
| Classic Class-F | Short | Open | 90.7% | ~1 to 5% | Narrowband, single channel |
| Continuous Class-F | Reactive arc (γ) | Open | 90.7% | 1.5:1 to 2:1 | 5G / multi-band base station |
| Continuous inverse Class-F | Reactive arc (γ) | Short | 90.7% | 1.5:1 to 2:1 | Compact, capacitive packages |
| Continuous Class-B/J | Reactive (γ) | Don't-care | 78.5% | > 2:1 (octave) | Wideband SDR / EW radios |
| Class-AB | Best-effort | Best-effort | 50 to 65% | Multi-octave | Linear, low complexity |
Frequently Asked Questions
How does a continuous Class-F mode differ from a classic Class-F amplifier?
Classic Class-F fixes the harmonic loads at one frequency: open at odd harmonics, short at even harmonics, giving an ideal 90.7% efficiency at a single point. The continuous mode adds a parameter γ from −1 to +1 that reshapes the fundamental and second-harmonic terminations together, so the 2nd-harmonic load walks a reactive arc instead of sitting at one short. Many impedance combinations now deliver identical efficiency, letting a network satisfy the condition over a 1.5:1 to 2:1 span while peak drain voltage stays within breakdown limits.
What is the role of the gamma parameter in continuous-mode design?
γ is the knob that sweeps the amplifier through the continuous family. The normalized drain voltage is v(θ) = (1 − α cosθ)(1 − γ sinθ) with α near 2/√3. At γ = 0 it collapses to the classic maximally flat Class-F solution. Sweeping γ rotates the fundamental impedance phase and moves Z2 around a reactive arc while peak voltage and 90.7% efficiency stay fixed, so each frequency can use its own γ and the matching network only has to land inside the continuum.
What bandwidth and efficiency can continuous-mode PAs realistically achieve?
GaN HEMT continuous-mode designs routinely cover 1.5 to 1.6:1 fractional bandwidth, and multi-mode implementations exceed 2:1 (for example 1.4 to 2.6 GHz). Measured drain efficiency holds 60 to 75% across the band with peaks above 80%, at 10 to 100 W saturated output depending on device periphery. A tuned Class-F may hit 80% at one frequency but drops below 50% within a few percent. The cost is added network complexity and slightly lower peak efficiency in exchange for usable efficiency across the whole band.