Why was the 'Continuous' design space invented?

Historically, switch-mode amplifiers like Class E/F2 required razor-sharp, exact impedances at the fundamental and harmonic frequencies to function (e.g., exactly 0 ohms at the 2nd harmonic). If the frequency shifted by even 5%, the exact impedance requirement was lost, efficiency plummeted, and the transistor blew up. This restricted switch-mode PAs to very narrow bandwidths. The Continuous Class EF framework proved mathematically that you don't need *exact* points; there is an entire 'space' of valid impedances that still satisfy ZVS conditions, allowing the amplifier to operate over a much wider frequency band.

How does Continuous Class EF increase bandwidth?

By mathematically mapping the valid impedance space on a Smith Chart, designers realized they could build a single matching network whose natural impedance curve (which changes with frequency) snakes precisely through the 'valid' zones of the continuous design space across an entire octave of bandwidth. The amplifier remains highly efficient and avoids destructive voltage spikes across the entire band, rather than just at one single frequency.

What is the physical difference between Class EF and Class E/F2?

Class E/F2 is a specific point-solution within the broader Class EF family. A physical Class E/F2 amplifier contains a highly specific L-C trap designed to short out the 2nd harmonic. A modern Continuous Class EF amplifier does not use discrete harmonic traps. Instead, it uses a complex, multi-section transmission line network that naturally presents a sweeping range of acceptable reactive impedances to the transistor across a wide bandwidth.

PA Architecture

Class EF Amplifier

A defense contractor needs a switch-mode power amplifier for a military radio that hops frequencies unpredictably between 1 GHz and 2 GHz. They cannot use a standard Class E or Class E/F2 amplifier, because those architectures rely on razor-sharp, highly specific harmonic traps that only work at a single frequency. When the radio hops from 1 GHz to 1.5 GHz, the narrowband traps fail, and the transistor burns up. The engineers solve this by designing a Continuous Class EF amplifier. Instead of demanding a specific, rigid impedance at the fundamental and harmonic frequencies, the mathematical framework of Continuous EF reveals a vast, flexible "design space" of acceptable impedances that still maintain Zero-Voltage Switching (ZVS) and low peak voltage. By designing a multi-section transmission line network that keeps the impedance inside this flexible "safe zone" across the entire 1-2 GHz spectrum, the radio can hop frequencies instantly without losing efficiency or destroying the transistor.

Category: PA Architecture

Design Framework: Continuous Mode (Broadband Design Space)

Primary Advantage: Octave-wide bandwidth for switch-mode PAs

The Evolution of Switch-Mode PA Design

Amplifier Architecture	Harmonic Impedance Requirement	Bandwidth Capability	Primary Application
Pure Class E	Reactance must be highly specific	Narrow (~5-10%)	Fixed-frequency transmitters
Class E/F2	Exact short (0 ohms) at 2nd harmonic	Very Narrow (<5%)	High-power, fixed frequency
Continuous Class EF	A flexible range of reactive values	Broadband (Octave or more)	Frequency-hopping / Multi-band

The Continuous Mode Phase Parameter (γ):
In standard amplifier theory, the fundamental voltage and current waveforms are locked in a specific phase relationship. In "Continuous" modes, a mathematical parameter (γ) is introduced. By sweeping γ between -1 and +1, the equations generate an infinite family of voltage and current waveforms that all yield identical theoretical efficiency.

Translating Phase to Impedance:
Because there are infinite valid waveforms, there are infinite valid fundamental and harmonic impedances. As long as the physical matching network's impedance trajectory (plotted on a Smith Chart as frequency changes) stays within the mathematically defined boundaries generated by the γ sweep, the amplifier will survive and operate efficiently across the entire band.

Common Questions

Frequently Asked Questions

Are there other 'Continuous' amplifier classes?

Yes. The breakthrough of continuous mode theory first revolutionized linear amplifiers with the invention of 'Continuous Class F' and 'Continuous Class B/J'. Once the mathematical framework proved that you could map flexible design spaces for linear amplifiers, researchers applied the exact same mathematics to switch-mode amplifiers, resulting in the Continuous Class EF family.

Does Continuous Class EF sacrifice efficiency for bandwidth?

Theoretically, no. The equations dictate that every point within the continuous design space yields the exact same maximum efficiency. However, practically, yes. Real-world transistors have nonlinear parasitic capacitances that change with voltage. Because the voltage waveform's shape changes as you move through the continuous space across the frequency band, the practical efficiency will fluctuate slightly (e.g., dropping from 85% to 75% at the band edges).

How do you design a Continuous Class EF network?

It cannot be done easily with standard Smith Chart tuning. It requires advanced EDA software (like Keysight ADS or AWR Microwave Office). Engineers use mathematical equations to plot the valid continuous impedance space as "target contours" on the Smith Chart. They then run optimization algorithms to synthesize a physical microstrip network that snakes its impedance curve perfectly through the center of those target contours from the lowest to the highest frequency.

Related Terms

← Class E/F2 Clearance →

PA Architecture

Continuous Design Space Generator

Input your transistor parameters and desired octave bandwidth. The tool will generate the continuous ZVS impedance contours for both the fundamental and 2nd harmonic, allowing you to synthesize a broadband, high-efficiency matching network.

Generate Impedance Contours