Amplifier Design

Available Gain Design

Q: How does available gain design differ from operating gain design?

In available gain design, the source impedance is selected first (for noise or other criteria), and the output network is then conjugate-matched to the resulting output impedance. In operating gain design, the load impedance is selected first (for power or linearity), and the input network is then conjugate-matched. Available gain design is the natural choice for LNA design because noise figure is determined by the source impedance, so choosing the source first allows direct control of noise performance. Operating gain design is preferred for power amplifier design where the load impedance determines output power and efficiency.

Q: What are noise circles and how are they used?

Noise circles are contours of constant noise figure plotted on the Smith chart in the source reflection coefficient (Γ_S) plane. The minimum noise figure point (Γ_opt) is at the center of the smallest circle. Successively larger circles represent higher noise figures (F_min + 0.5 dB, F_min + 1 dB, etc.). By overlaying noise circles with available gain circles on the same Smith chart, the designer can visualize the trade-off between noise figure and gain, selecting a source impedance that achieves an acceptable compromise.

Q: Why can't you achieve maximum gain and minimum noise figure simultaneously?

Maximum gain requires a conjugate match at the input: Γ_S = S11* (or the stability-corrected equivalent Γ_MS). Minimum noise figure requires Γ_S = Γ_opt, the optimum noise source impedance from the transistor's noise parameters. In general, Γ_opt ≠ S11*, so the source impedance that maximizes gain is different from the one that minimizes noise. The available gain design method allows the designer to choose Γ_S = Γ_opt for minimum noise, accepting a gain reduction (typically 1-3 dB below maximum available gain), then recover some output power by conjugate-matching the output.

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A microwave amplifier design method where the source reflection coefficient (Γ_S) is chosen first, typically for minimum noise figure, and then the output matching network is designed to conjugate-match the resulting output impedance. This decouples noise optimization from output matching, making it the standard approach for LNA design. The trade-off between noise figure and gain is visualized by overlaying noise circles and available gain circles on the Smith chart.

Category: Amplifier Design

Optimizes: Noise figure via Γ_S

Output: Conjugate matched

Understanding Available Gain Design

In any two-port amplifier, the noise figure depends primarily on the source impedance presented to the transistor's input. The transistor's noise parameters (F_min, R_n, Γ_opt) define how noise figure varies with source impedance: minimum noise figure F_min occurs when Γ_S = Γ_opt, and noise increases as Γ_S moves away from Γ_opt. The available gain design method takes advantage of this by selecting the source impedance for noise performance, then accepting whatever gain results from that choice and recovering output power through conjugate matching.

The design flow proceeds in four steps: (1) Plot noise circles and available gain circles on the source (Γ_S) Smith chart. (2) Choose Γ_S at or near Γ_opt for minimum noise, noting the corresponding available gain. (3) Calculate the output reflection coefficient Γ_out that results from the chosen Γ_S. (4) Design the output matching network to present Γ_L = Γ_out* (conjugate match) to extract maximum power. The resulting amplifier achieves minimum noise figure with the maximum gain possible for that noise condition.

Available Gain Design Equations

Available Gain (for given Γ_S):
G_A = (1 − |Γ_S|²) × |S₂₁|² / (|1 − S₁₁Γ_S|² × (1 − |Γ_out|²))

Output Reflection Coefficient:
Γ_out = S₂₂ + S₁₂S₂₁Γ_S / (1 − S₁₁Γ_S)

Noise Figure vs. Source Impedance:
F = F_min + (4R_n/Z₀) × |Γ_S − Γ_opt|² / ((1 − |Γ_S|²) × |1 + Γ_opt|²)

Output Conjugate Match:
Γ_L = Γ_out* (for maximum power transfer from output)

Available Gain vs. Operating Gain Design

Aspect	Available Gain Design	Operating Gain Design
First Choice	Source impedance (Γ_S)	Load impedance (Γ_L)
Optimizes	Noise figure	Output power / linearity
Second Match	Output conjugate matched	Input conjugate matched
Smith Chart	Noise + gain circles in Γ_S plane	Gain + power circles in Γ_L plane
Best For	LNA, receiver front-end	PA, driver amplifier
Gain Sacrifice	1-3 dB below MAG typically	None (gain maximized)

Common Questions

Frequently Asked Questions

How does available gain design differ from operating gain design?

Available gain design selects the source impedance first (for noise), then conjugate-matches the output. Operating gain design selects the load first (for power/linearity), then conjugate-matches the input. Available gain is natural for LNA design where noise figure is set by the source. Operating gain is preferred for PAs where load impedance determines output power and efficiency.

What are noise circles and how are they used?

Noise circles are contours of constant noise figure on the Smith chart in the Γ_S plane. The minimum noise figure point Γ_opt is at the center. Larger circles represent higher noise figures. Overlaying noise circles with available gain circles lets the designer visualize the noise-gain trade-off and select a source impedance that achieves an acceptable compromise between minimum noise and maximum gain.

Why can't you achieve maximum gain and minimum noise figure simultaneously?

Maximum gain requires Γ_S = S₁₁* (conjugate match). Minimum noise requires Γ_S = Γ_opt. In general these are different impedances, so you must choose: noise-optimal source impedance with reduced gain (available gain design for LNAs), or gain-optimal source with higher noise (for driver stages where noise is not the priority).

Related Terms

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