Microwave Transistors Study Guide

EEE 566 - Microwave Engineering

fT Analysis
S-Parameters
Stability Circles

1. Types of Microwave Transistors

BJT (Bipolar)

Si/Ge

Bipolar Junction Transistors use both electron and hole charge carriers. At microwave frequencies, they suffer from base transit time limitations and parasitic capacitances.

fT ≈ 1 / (2πτec)
  • High current gain (β)
  • Low flicker noise
  • Limited by base transit time
  • Typical fmax: 10-50 GHz
Structure
Emitter (n+) Base (p) Collector (n)

HBT (Heterojunction)

III-V

Uses different semiconductor materials for emitter and base (e.g., AlGaAs/GaAs). The heterojunction provides high emitter injection efficiency and lower base resistance.

fmax = √(fT / 8πRbCbc)
  • Higher fT than BJT
  • Excellent high-frequency noise
  • GaAs or InP based
  • Typical fmax: >100 GHz
Bandgap Engineering
Wide Gap
Emitter
→
Narrow Gap
Base

MESFET

GaAs

Metal-Semiconductor Field Effect Transistor. Uses a Schottky barrier gate to control current flow in the n-type channel. Unipolar device (electrons only).

fT = gm / 2π(Cgs + Cgd)
  • No minority carrier storage
  • High input impedance
  • Negative drain conductance possible
  • Depletion mode operation
Source
Drain
Gate (Schottky)

HEMT / pHEMT

2DEG

High Electron Mobility Transistor (also called MODFET). Uses a heterojunction to create a 2-Dimensional Electron Gas (2DEG) channel with extremely high mobility.

fmax = (fT/2) × √(Rds/(Ri+Rg+Rs))
  • Highest frequency operation
  • Low noise figure (excellent for LNAs)
  • High power added efficiency
  • Typical fmax: >500 GHz
Modulation Doping
AlGaAs(Supply layer)
2DEG Channel(High mobility)
GaAs Buffer(Substrate)

2. Scattering Parameters (S-Parameters)

At microwave frequencies, open and short circuit conditions are difficult to realize due to parasitic inductances and capacitances. S-parameters characterize devices using traveling waves with matched terminations (typically 50Ω).

Two-Port S-Matrix

[b] = [S][a]
S11 = b1/a1 |a2=0
Input Reflection
S21 = b2/a1 |a2=0
Forward Transmission
S12 = b1/a2 |a1=0
Reverse Transmission
S22 = b2/a2 |a1=0
Output Reflection

Key Properties:

  • ▸ Reciprocal: Sij = Sji (for passive networks)
  • ▸ Lossless: [S]T[S]* = [I] (Unitary matrix)
  • ▸ Power Gain: |S21|2 represents power gain for matched load

Visual Representation

[S] a₁ b₁ a₂ b₂ Two-Port Network Port 1 (Input) Port 2 (Output)
Incident (a) and reflected (b) waves at each port

3. Design Calculators

Gain-Bandwidth Calculator

fT (Cutoff)
12.0 GHz
Transit Frequency
fmax (Max Oscillation)
89.5 GHz
Power Gain = 1
fT = gm / 2π(Cgs + Cgd)

Stability Analysis (Rollet's Factor)

Rollet's Stability Factor (K) 1.25
|Δ| 0.23
Unconditionally Stable
Condition: K > 1 AND |Δ| < 1

Noise Figure & Source Reflection Coefficient

Noise Figure Circle
1.5 dB
At Γopt (minimum noise)
Constant Noise Circles:
N = (F - Fmin)/4Rn × |1 + Γopt|2

4. Biasing and Stability Considerations

Stability Criteria

A transistor is unconditionally stable if for all passive source and load impedances, the real part of the input and output impedances remains positive.

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

Potential Instability

If K < 1, the device is potentially unstable. Stability circles must be drawn on the Smith Chart to identify "forbidden" regions for ΓS and ΓL.

  • • Input Stability Circle: Centers at CI, radius rI
  • • Output Stability Circle: Centers at CL, radius rL
  • • Stable region depends on |S11| and |S22|

Biasing Techniques

FET Biasing

Self-bias: Source resistor (RS) creates negative gate-source voltage via voltage drop.
Active bias: Uses operational amplifiers for precise gate voltage control.

BJT Biasing

Fixed bias: Simple but thermally unstable.
Voltage divider bias: More stable against β variations.
Active bias: Maintains constant collector current.

Design Trade-offs

Maximum Gain ↔ Conjugate Matching
Minimum Noise ↔ Γs = Γopt
Stability ↔ Avoid stability circles
Bandwidth ↔ Compromise matching

Transistor Comparison Summary

Parameter Si BJT HBT MESFET HEMT
fmax Range 10-50 GHz 50-200 GHz 20-100 GHz >500 GHz
Noise Figure Moderate (1-3 dB) Low (0.5-2 dB) Low (1-2 dB) Very Low (0.3-1 dB)
Power Handling High High Medium Medium-High
Input Impedance Low (~50Ω) Low (~50Ω) High High
Primary Use Power amps, drivers Oscillators, mixers General purpose RF LNA, mmWave