1 / 15

Microwave Transistors

High-Frequency Semiconductor Devices & Amplifier Design

BJT • FET • HEMT • HBT • S-Parameters • Stability • Noise

Undergraduate Microwave Engineering Course

Learning Objectives

01

Device Physics

Understand operation of BJTs and FETs at microwave frequencies

02

S-Parameters

Master scattering parameters for transistor characterization

03

Gain Analysis

Calculate transducer, available, and operating power gains

04

Stability Design

Analyze stability circles and design for unconditional stability

05

Noise & Biasing

Optimize noise figure and design DC bias networks for microwave transistors

Why Microwave Transistors?

Traditional low-frequency transistor models fail at microwave frequencies (>1 GHz) due to:

  • Parasitic capacitances and inductances
  • Transit time limitations
  • Skin effect and distributed parameters
  • Wave propagation effects

Microwave transistors are optimized for high-frequency operation with minimized parasitics and specialized structures like heterojunctions.

FREQUENCY SPECTRUM 1MHz 1GHz 10GHz 100GHz RF MICROWAVE mmWave BJT/FET

BJT vs FET at Microwave Frequencies

Bipolar Junction Transistor (BJT)

Control Mechanism Current (Base)
Input Impedance Low (~kΩ)
Noise Figure Low (0.5-2dB)
fT Limit ~50 GHz

Best for: Low noise amplifiers (LNA), oscillators below X-band

Field Effect Transistor (FET/HEMT)

Control Mechanism Voltage (Gate)
Input Impedance High (~MΩ)
Noise Figure Very Low (0.2-1dB)
fT Limit >100 GHz

Best for: High-frequency amps, power amps, mixers, switches

At microwave frequencies, FETs generally outperform BJTs due to higher input impedance and better high-frequency response

High-Frequency Small-Signal Model

HYBRID-π EQUIVALENT CIRCUIT Base (B) rbb' B' Cπ rπ Emitter (E) gmVπ ↓ Cμ ro Collector (C) Miller ×(1+Av)

Key Parameters

  • • rbb': Base spreading resistance
  • • Cπ: Base-emitter capacitance
  • • Cμ: Base-collector capacitance (Miller)
  • • gm: Transconductance

Transition Frequency

fT = gm / 2π(Cπ + Cμ)

Frequency where current gain = 1

Maximum Frequency

fmax ≈ √(fT / 8πrbb'Cμ)

Unity power gain frequency

Scattering Parameters (S-Parameters)

At microwave frequencies, impedance (Z) and admittance (Y) parameters are difficult to measure because:

  • Open and short circuits are difficult to realize (parasitics)
  • Active devices may oscillate under open/short conditions
  • Transmission line effects dominate

Solution: S-parameters use matched loads (Z₀ = 50Ω) as reference, which are easy to implement and stable.

2-PORT NETWORK REPRESENTATION [S] a₁ b₁ a₂ b₂ a = Incident wave (V⁺/√Z₀) b = Reflected wave (V⁻/√Z₀)
S₁₁
Input Reflection
S₂₁
Forward Transmission
S₁₂
Reverse Transmission
S₂₂
Output Reflection

The S-Parameter Matrix

b₁ = S₁₁a₁ + S₁₂a₂
b₂ = S₂₁a₁ + S₂₂a₂
→
[b₁] [S₁₁ S₁₂] [a₁]
[b₂] = [S₂₁ S₂₂] [a₂]

Physical Interpretation

S₁₁ Input reflection with output matched (a₂=0)
S₂₂ Output reflection with input matched (a₁=0)
S₂₁ Forward transmission (gain) with output matched
S₁₂ Reverse transmission (isolation) with input matched

Key Relationships

Input Reflection Coefficient:
Γin = S₁₁ + (S₁₂S₂₁ΓL)/(1-S₂₂ΓL)
Output Reflection Coefficient:
Γout = S₂₂ + (S₁₂S₂₁ΓS)/(1-S₁₁ΓS)
Unilateral Approximation (S₁₂≈0):
Γin ≈ S₁₁, Γout ≈ S₂₂

Transistor Power Gains

Operating Power Gain

GP = PL/Pin

Power delivered to load divided by power input to network

|S₂₁|²(1-|ΓL|²)
GP = ----------------
|1-S₂₂ΓL|²(1-|Γin|²)

Available Power Gain

GA = Pavn/Pavs

Power available from network divided by power available from source

|S₂₁|²(1-|ΓS|²)
GA = ----------------
|1-S₁₁ΓS|²(1-|Γout|²)

Transducer Gain

GT = PL/Pavs

Power delivered to load divided by power available from source

|S₂₁|²(1-|ΓS|²)(1-|ΓL|²)
GT = -----------------------------
|(1-S₁₁ΓS)(1-S₂₂ΓL)-S₁₂S₂₁ΓSΓL|²

Maximum Unilateral Transducer Gain

GTU,max = GS · G0 · GL
When ΓS = S₁₁* and ΓL = S₂₂*
GS = 1/(1-|S₁₁|²) (Input match)
G0 = |S₂₁|² (Intrinsic gain)
GL = 1/(1-|S₂₂|²) (Output match)

Stability Analysis

A transistor amplifier must be unconditionally stable for all passive source and load impedances.

Rollet's Stability Factor (K)

K = (1-|S₁₁|²-|S₂₂|²+|Δ|²) / (2|S₁₂S₂₁|)
where Δ = S₁₁S₂₂ - S₁₂S₂₁

Unconditional Stability: K > 1 AND |Δ| < 1

μ-Parameter (Alternative)

μ = (1-|S₁₁|²) / (|S₂₂-ΔS₁₁*|+|S₁₂S₂₁|)

Stability: μ > 1 (simpler single-parameter test)

Stability Circles

Input Stability Output Stability Center Stable

Smith Chart showing stability circles (unstable regions outside)

Stabilization Techniques

Resistive Loading

Source Rstab Transistor Load
  • • Add series or shunt resistor at input/output
  • • Trade-off: Reduces gain, increases noise
  • • Typically 50-200Ω resistors

Feedback Techniques

In Out Lfb
  • • Inductive degeneration (common source)
  • • Neutralization (cancel Cgd)
  • • Advantage: Better noise figure than resistive

Design Rule: Always check stability across entire frequency band (not just design frequency). Use K > 1.2 for margin.

Noise Figure Optimization

Friis Formula for Cascaded Stages

Ftotal = F₁ + (F₂-1)/G₁ + (F₃-1)/(G₁G₂) + ...

The first stage dominates the noise figure → LNA design is critical

Transistor Noise Parameters

Minimum Noise Figure:
Fmin
Optimal Source Reflection:
Γopt
Noise Resistance:
Rn (sensitivity to mismatch)

Design Trade-off: Γopt (for Fmin) ≠ S₁₁* (for max gain). Must compromise between noise and gain.

Noise Circles

Γopt Gain Smith Chart: Noise & Gain F > Fmin
Constant Noise Figure circles
Constant Gain circles

DC Biasing Networks

FET Biasing (Common Source)

RFC RFC Cb Gate Drain Source VDD
  • • RFC (Radio Frequency Choke): Blocks AC, passes DC
  • • Bypass Capacitor: Shorts AC to ground
  • • Set VGS for desired ID (check I-V curves)

BJT Biasing

Active Biasing

Uses feedback to maintain constant collector current over temperature. More complex but stable.

Passive Biasing (Voltage Divider)

Resistive network sets base voltage. Simple but temperature sensitive.

Design Considerations

  • • Bypass all bias lines to ground
  • • Use high-Q inductors for RFCs
  • • Keep bias lines λ/4 away from active device

Advanced Microwave Transistors

HEMT (High Electron Mobility)

2DEG
  • • Heterojunction (AlGaAs/GaAs)
  • • 2D electron gas channel
  • • fT > 100 GHz
  • • Ultra-low noise (0.3 dB @ 12 GHz)

pHEMT (Pseudomorphic)

InGaAs
  • • InGaAs channel (lattice mismatch)
  • • Higher electron mobility
  • • fT > 200 GHz
  • • Power applications (GaN pHEMT)

HBT (Heterojunction Bipolar)

SiGe/GaAs
  • • Wide bandgap emitter
  • • High current gain (β > 100)
  • • 1/f noise better than FET
  • • Excellent for oscillators
GaAs
Substrate Material
InP
High Frequency
GaN
High Power
SiGe
Low Cost

Amplifier Design Example

Design Specifications

Freq: 2.4 GHz
Gain: >15 dB
NF: <2 dB
Z₀: 50Ω

Transistor S-Params @ 2.4GHz

S₁₁0.65∠-95°
S₂₁3.2∠110°
S₁₂0.08∠35°
S₂₂0.45∠-45°
K1.25

Design Steps

  1. Check stability: K=1.25>1 ✓ Stable
  2. Calculate max gain: GT,max ≈ 16 dB
  3. Input match: ΓS = S₁₁* = 0.65∠95°
  4. Output match: ΓL = S₂₂* = 0.45∠45°
  5. Design matching networks (L-section or stub)

Amplifier Schematic

Input Match FET Output Match Source 50Ω Load 50Ω VGS VDS Simulated Performance Gain: 16.2 dB | NF: 1.8 dB | P1dB: 18 dBm

Key Takeaways

1

S-Parameters Essential

Use S-parameters for all microwave transistor characterization. Z/Y parameters fail at high frequencies.

2

Stability First

Always check K > 1 and |Δ| < 1. Use resistive loading or feedback if potentially unstable.

3

Gain vs Noise Trade-off

Simultaneous conjugate match gives max gain but not min noise. Compromise based on application.

4

Device Selection

HEMTs for ultra-low noise and high frequency. HBTs for high gain and oscillators. BJTs for cost-sensitive designs.

Questions?

Microwave Engineering • Transistor Amplifiers • High-Frequency Design