RF Design

Current Waveform

Q: How does conduction angle change the drain current waveform?

The conduction angle is the portion of each RF cycle during which the device draws current. A 360-degree angle gives a full sinusoidal waveform (Class A), 180 to 360 degrees gives a partially truncated sine (Class AB), 180 degrees gives a half-sine pulse (Class B), and angles below 180 degrees down to near zero produce sharp current spikes (Class C). As the conduction angle narrows, the fundamental-frequency component first rises slightly and then falls, while the DC component drops faster, so theoretical drain efficiency climbs from 50 percent at Class A to 78.5 percent at Class B and toward 100 percent as Class C current pulses approach an impulse. Narrower angles also generate stronger harmonics that must be managed by the output network.

Q: Why does a Class F amplifier use a square current waveform?

In an ideal Class F amplifier the voltage waveform is shaped into a square wave while the current is held as a half-sine, so that voltage and current never overlap and dissipation falls toward zero. Inverse Class F (Class F-1) flips this: the current is shaped toward a square wave and the voltage becomes a half-sine. The square current waveform is built by presenting an open circuit at even harmonics and a short circuit at odd harmonics at the device current generator plane: the open at even harmonics blocks even-harmonic current and sustains the even-harmonic voltage that rounds the voltage into a half-sine, while the short at odd harmonics suppresses odd-harmonic voltage and lets the odd-harmonic current that builds the square pulse circulate freely. In practice only the second and third harmonics are controlled, which still raises drain efficiency to roughly 80 to 88 percent versus about 78.5 percent for ideal Class B.

Q: How is the current waveform measured at the device intrinsic plane?

You cannot probe the intrinsic current generator directly, so engineers reconstruct the waveform using waveform-engineering load-pull. A calibrated sampling oscilloscope or large-signal network analyzer captures the magnitude and phase of voltage and current at the fundamental and several harmonics at the package reference plane, then a de-embedding model removes the parasitic shunt capacitance, bond-wire inductance, and access resistance to refer the data back to the intrinsic plane. The resulting time-domain current and voltage trajectories reveal whether the device is operating in the intended class and whether the harmonic terminations are producing the desired square, half-sine, or peaked current shape.

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Plotted against time over one RF cycle, the drain or collector current of an active device traces a shape whose conduction angle, peak amplitude, and harmonic content define how an amplifier behaves. Reducing the angle from a full 360° sinusoid (Class A) to a 180° half-sine (Class B) or a narrow Class C pulse trades linearity for efficiency, while deliberate harmonic shaping through waveform engineering drives high-efficiency modes. Together with the device load line, the current shape sets where voltage and current overlap and therefore how much DC power is dissipated as heat rather than delivered as RF.

Category: RF Design

Class A η: 50% (max)

Class B η: 78.5% (max)

Reading the Drain Current as a Time-Domain Signal

At RF and microwave frequencies, the instantaneous current through a transistor channel is not a clean replica of the input. The device acts as a controlled current source whose output is gated by the gate or base drive and clipped by pinch-off and saturation. Capturing that current as a function of time over a single period produces the current waveform, the single most diagnostic view of how a power amplifier actually operates. Its shape reveals the bias point, the conduction angle, the degree of compression, and the harmonic energy the output network must terminate.

The classical amplifier classes are defined directly by this waveform. A Class A stage biased at half the maximum current conducts for the full cycle and produces an undistorted sinusoid, but it dissipates DC power even with no input, capping drain efficiency at 50 percent. Pulling the bias toward pinch-off truncates the bottom of the sinusoid into a half-sine (Class B, 180° conduction) or a narrow pulse (Class C, below 180°). As the pulse narrows the DC current falls faster than the useful fundamental component, so efficiency rises even though the raw waveform looks increasingly distorted.

That distortion is not waste if it is managed. Each truncated current pulse is rich in harmonics, and by presenting specific reactive terminations at the second and third harmonics, a designer can reshape the companion voltage waveform so that voltage and current never peak together. This is the basis of switched-mode and harmonically-tuned classes such as Class E and Class F, where the current waveform is engineered as deliberately as the matching network.

Fourier Decomposition and Conduction Angle

Because the current pulse repeats every RF cycle it is periodic, so a Fourier series expresses it as a DC term plus harmonics of the fundamental. The coefficients depend only on the conduction angle 2α, which makes the angle the master variable that links waveform shape to efficiency.

Reduced-conduction-angle current pulse:
i_D(θ) = I_max × (cosθ − cosα) / (1 − cosα), for |θ| ≤ α

DC and fundamental components:
I_DC = (I_max / 2π) × (2sinα − 2α·cosα) / (1 − cosα)
I₁ = (I_max / 2π) × (2α − sin2α) / (1 − cosα)

Drain efficiency:
η = ½ × (V₁ / V_DD) × (I₁ / I_DC)

Where θ = instantaneous phase, 2α = conduction angle, I_max = peak device current, V₁ = fundamental voltage swing, V_DD = supply. At α = 90° (Class B) the I₁/I_DC ratio ≈ π/2, giving η_max ≈ 78.5%.

Current Waveform by Amplifier Class

Class	Conduction Angle	Current Shape	Bias Point	Max Drain η	Linearity
A	360°	Full sinusoid	50% I_max	50%	Excellent
AB	180° to 360°	Truncated sine	5 to 30% I_max	50 to 78.5%	Good
B	180°	Half-sine	Pinch-off	78.5%	Moderate
C	< 180°	Narrow pulse	Below pinch-off	78.5 to ~100%	Poor
F	180° (shaped)	Half-sine, square voltage	Pinch-off	80 to 88%	Poor (switched)
F^-1	180° (shaped)	Square current	Pinch-off	80 to 90%	Poor (switched)

Common Questions

Frequently Asked Questions

How does conduction angle change the drain current waveform?

The conduction angle is the fraction of each RF cycle in which the device draws current. A 360° angle gives a full sine (Class A), 180° a half-sine (Class B), and angles below 180° sharp Class C spikes. As the angle narrows, I_DC falls faster than the fundamental I₁, so theoretical efficiency climbs from 50% (Class A) to 78.5% (Class B) toward 100% as the pulse approaches an impulse, at the cost of stronger harmonics that the output network must terminate.

Why does a Class F amplifier use a square current waveform?

Ideal Class F shapes the voltage into a square wave while keeping current a half-sine so they never overlap and dissipation falls toward zero. Inverse Class F (F^-1) reverses this, shaping the current toward a square wave. The square current is built by terminating even harmonics in an open and odd harmonics in a short at the current-generator plane. Controlling just the 2nd and 3rd harmonics still lifts drain efficiency to roughly 80 to 88% versus 78.5% for ideal Class B.

How is the current waveform measured at the device intrinsic plane?

The intrinsic current generator cannot be probed directly, so engineers reconstruct it with waveform-engineering load-pull. A large-signal network analyzer or sampling scope captures voltage and current magnitude and phase at the fundamental and several harmonics at the package plane, then a de-embedding model strips shunt C_ds, bond-wire inductance, and access resistance to refer the data to the intrinsic plane. The recovered time-domain trajectory shows whether the harmonic terminations produced the intended square, half-sine, or peaked shape.

Related Terms

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