What are the three amplifier configurations and their RF trade-offs?

The three fundamental bipolar transistor configurations each optimize for different RF requirements. Common Emitter (CE): input at base, output at collector, emitter grounded (or with degeneration). Provides both voltage and current gain. Voltage gain A_v = -gm * R_C (inverted output). Input impedance: r_pi = beta/gm (moderate, typically 500 ohms to 5 kohm). Bandwidth limited by Miller multiplication of C_mu: effective input capacitance = C_pi + C_mu*(1+|A_v|). Standard configuration for RF gain stages. Common Base (CB): input at emitter, output at collector, base grounded (AC). Current gain approximately 1 (alpha = beta/(beta+1) ≈ 0.98-0.99). Voltage gain: gm * R_C (non-inverted). No Miller effect on C_mu since base is grounded, giving much wider bandwidth than CE. Input impedance: 1/gm (very low, 5-25 ohms). Used for wideband amplifiers and as cascode upper device. Excellent reverse isolation (S12 very small). Common Collector (CC, emitter follower): input at base, output at emitter. Voltage gain approximately 1 (buffer). High input impedance: r_pi * (1 + gm*R_E). Low output impedance: 1/gm + R_S/beta. Used as impedance buffer between stages and for driving low-impedance loads. Bandwidth is high because there is no voltage gain to cause Miller multiplication.

How does the hybrid-pi model work for RF analysis?

The hybrid-pi model is the standard small-signal equivalent circuit for bipolar transistors at RF frequencies. It replaces the physical transistor with a network of linear elements valid for small signals around the DC operating point. Key elements: gm (transconductance) = I_C/V_T where V_T = kT/q = 25.85 mV at 25 degrees C. This is the controlled current source: i_c = gm * v_be. r_pi (base-emitter resistance) = beta/gm = V_T*beta/I_C. At I_C = 1 mA, beta = 100: r_pi = 2.585 kohm. C_pi (base-emitter capacitance) = includes diffusion capacitance (C_D = gm*tau_F where tau_F is forward transit time) plus depletion capacitance. Dominant at high frequencies, sets fT. C_mu (collector-base capacitance) = depletion capacitance of reverse-biased CB junction. Typically 0.1-2 pF. Causes Miller effect in CE configuration. r_bb' (base spreading resistance) = physical resistance of the base semiconductor region from contact to active area. Typically 5-50 ohms. Critical for noise performance: contributes thermal noise that directly adds to NF_min. r_o (output resistance) = V_A/I_C where V_A is the Early voltage. Typically 10-100 kohm. Models finite output impedance (slope of I_C vs V_CE curves). At frequencies above fT/10, the parasitic elements (C_pi, C_mu, r_bb') dominate circuit behavior, and the hybrid-pi model becomes essential for accurate design.

What determines the noise figure of a bipolar transistor amplifier?

The minimum noise figure of a bipolar transistor is determined by several physical mechanisms. Shot noise: the collector current consists of discrete electrons crossing the base-emitter junction. Shot noise current spectral density: i_n^2 = 2*q*I_C (A^2/Hz). Base current also has shot noise: i_nb^2 = 2*q*I_B = 2*q*I_C/beta. Thermal noise: base resistance r_bb' generates thermal noise voltage: v_n^2 = 4*k*T*r_bb' (V^2/Hz). This is often the dominant noise source and is why HBTs with low r_bb' achieve better NF. The minimum noise figure expression (simplified): NF_min ≈ 1 + (1/beta) + 2*sqrt(f/fT * (1/beta + r_bb'*gm*(f/fT))). Key observations: NF_min increases with frequency (approximately linearly with f/fT). Lower r_bb' reduces NF_min (SiGe HBTs with r_bb' = 5-15 ohms vs. 30-100 ohms for Si BJTs). There is an optimum collector current for minimum NF: too low reduces gm (less gain, more noise from following stages), too high increases shot noise. Typical optimum: I_C = 2-10 mA for RF LNAs. The noise figure also depends on source impedance matching: NF = NF_min only when the source impedance equals the optimum noise impedance Z_opt. Simultaneous noise and power matching is generally not possible, requiring compromise or feedback techniques.

Active Device / Semiconductor

Bipolar Transistor

/by-POH-lur tran-ZIS-tur/

Three-terminal semiconductor (NPN or PNP) using dual-carrier (electron + hole) conduction for current-controlled amplification. I_C = β·I_B, g_m = I_C/V_T = 38.7 mS/mA. Hybrid-pi model standard for RF analysis: C_π sets f_T, C_μ causes Miller effect, r_bb' dominates noise.

β: 20–500

g_m: I_C/V_T

Configs: CE, CB, CC

Understanding Bipolar Transistors for RF

The bipolar transistor's name reflects its use of both carrier types: electrons and holes participate in conduction, unlike FETs which are unipolar. In an NPN device, electrons injected from the emitter traverse the thin base region and are collected at the collector. The base current controls the rate of injection, providing current amplification with gain β = I_C/I_B.

For RF circuit design, the small-signal hybrid-pi model replaces the nonlinear transistor with a linear network of resistors, capacitors, and a controlled current source. This model accurately predicts gain, bandwidth, impedance, and noise performance up to frequencies approaching f_T.

Hybrid-Pi Model Elements

Transconductance:
g_m = I_C/V_T, V_T = kT/q = 25.85 mV (25°C)

Base-Emitter Resistance:
r_π = β/g_m = V_T·β/I_C

Capacitances:
C_π = C_D + C_je = g_mτ_F + C_depl
C_μ = 0.1–2 pF (CB depletion)

Transition Frequency:
f_T = g_m/(2πC_π)

Amplifier Configuration Comparison

Config	Gain	Z_in	Z_out	BW	Best For
CE	A_v = −g_mR_C	r_π (mod.)	R_C (mod.)	Miller-limited	Standard gain stage
CB	A_v = g_mR_C	1/g_m (low)	R_C (high)	Widest (no Miller)	Wideband, cascode top
CC	A_v ≈ 1	r_π(1+g_mR_E)	1/g_m (low)	High	Impedance buffer

Noise Figure Contributors

Source	Mechanism	Spectral Density	Mitigation
I_C shot	Discrete electrons	2qI_C	Optimize I_C
I_B shot	Base recombination	2qI_C/β	High-β device
r_bb' thermal	Base resistance	4kTr_bb'	Low r_bb' (HBT)

Common Questions

Frequently Asked Questions

Three configurations?

CE: voltage + current gain, Miller-limited BW. CB: voltage gain, wideband (no Miller), low Z_in = 1/g_m. CC (emitter follower): unity voltage gain, high Z_in, low Z_out buffer. Cascode = CE + CB for gain + bandwidth.

Hybrid-pi model?

g_m = I_C/V_T (controlled source), r_π = β/g_m (input R), C_π (sets f_T), C_μ (Miller effect in CE), r_bb' (base resistance, noise-critical). Valid for small signals up to ~f_T/10.

Noise figure?

NF_min ≈ 1 + (1/β) + 2√(f/f_T·(1/β + r_bb'g_mf/f_T)). Dominated by r_bb' thermal noise. Optimum I_C = 2–10 mA for LNAs. Noise match (Z_opt) differs from power match (S₁₁*).

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