Directional Coupler

Virtual Laboratory for Microwave Engineering

Interactive S-Parameters Smith Chart Analysis Power Flow Visualization

1 Learning Objectives

Understand the fundamental operation and physical construction of directional couplers

Analyze S-parameters and scattering matrix representation of 4-port networks

Calculate coupling factor, directivity, and isolation using measured power levels

Visualize power flow and wave propagation in coupled transmission lines

Design couplers with specific coupling values for microwave applications

Evaluate performance metrics: Return Loss, Insertion Loss, and VSWR

2 Theoretical Background

Principle of Operation

A directional coupler is a 4-port passive device that samples a small amount of microwave power for measurement purposes. It consists of two transmission lines (main line and coupled line) with electromagnetic coupling between them. The device is reciprocal, matched, and lossless (ideally), with power flowing from Port 1 to Port 2 (through), Port 3 (coupled), and ideally zero power to Port 4 (isolated).

Scattering Matrix (S-Parameters)

For a symmetric, reciprocal, matched, and lossless directional coupler, the S-matrix is:

[S] = -j ⎡ 0 √P √C 0 ⎤
⎢ √P 0 0 √C ⎥
⎢ √C 0 0 √P ⎥
⎣ 0 √C √P 0 ⎦

Where P = Power transmission coefficient, C = Coupling coefficient, P + C = 1

Coupling Factor (C)

Ratio of input power to coupled power (in dB):

C(dB) = 10 log₁₀(P₁/P₃)

Typical values: 3dB, 6dB, 10dB, 20dB, 30dB

Directivity (D)

Ratio of coupled power to isolated power:

D(dB) = 10 log₁₀(P₃/P₄)

Higher is better (typically 20-40 dB)

Isolation (I)

Ratio of input power to isolated power:

I(dB) = 10 log₁₀(P₁/P₄) = C + D

Insertion Loss

Power loss in the main line:

IL(dB) = 10 log₁₀(P₁/P₂) ≈ -10 log₁₀(1-C)

Common Configurations

  • Microstrip Coupled Lines: Edge-coupled or broadside-coupled parallel lines
  • Branch-Line Coupler: Two transmission lines connected by λ/4 branches (quadrature hybrid)
  • Lange Coupler: Interdigitated fingers for tight coupling (3dB)
  • Waveguide Bethe Hole: Single hole coupling between two waveguides

3 Laboratory Procedure

1

Setup and Calibration

Connect the directional coupler to the signal generator (Port 1) and spectrum analyzer. Set the operating frequency to 2.4 GHz (ISM band) or desired frequency. Ensure all ports are terminated with 50Ω loads except the measured port.

2

Measure Coupling Factor

Apply input power P₁ to Port 1. Measure power at Port 3 (coupled port) using P₃. Calculate coupling factor: C(dB) = 10 log₁₀(P₁/P₃). Record values for different frequencies across the band.

3

Measure Directivity

With input at Port 1, measure power at Port 4 (isolated port) using P₄. Calculate directivity: D(dB) = 10 log₁₀(P₃/P₄). This indicates how well the coupler discriminates between forward and reverse waves.

4

Measure Insertion Loss

Measure power at Port 2 (through port) using P₂. Calculate insertion loss: IL(dB) = 10 log₁₀(P₁/P₂). Verify that IL ≈ Coupling Loss (theoretical minimum based on coupling factor).

5

Return Loss Measurement

Measure reflected power at Port 1 to calculate return loss and VSWR. Ideally, input return loss should be >20 dB (VSWR < 1.2) for a well-matched coupler.

6

Frequency Sweep Analysis

Perform frequency sweep from 1-4 GHz to observe bandwidth characteristics. Plot coupling, directivity, and isolation vs. frequency. Identify the center frequency and 1-dB bandwidth.

Safety Note: Ensure power levels do not exceed device ratings (+20 dBm typical). Use proper ESD precautions when handling microwave components.

4 Interactive Simulation

Input Parameters

0 dBm 10 dBm 30 dBm
10 dB 30 dB 50 dB
1 GHz 2.4 GHz 4 GHz

Power Distribution Analysis

Port 2: Through
9.54 dBm
89.1 mW
Port 3: Coupled
0.00 dBm
1.0 mW
Port 4: Isolated
-30.00 dBm
0.001 mW
Insertion Loss
0.46 dB
Theoretical minimum
Coupling Region (λ/4) 1 (Input) 10 dBm 2 (Through) 9.54 dBm 3 (Coupled) 0 dBm 4 (Isolated) -30 dBm

Frequency Response

S-Parameter Magnitude

5 Design Calculator

Edge-Coupled Microstrip Design

Calculated Parameters

Even-mode Impedance (Z₀ₑ): 69.4 Ω
Odd-mode Impedance (Z₀ₒ): 36.0 Ω
Coupling Coefficient (k): 0.316
Coupled Line Length: 20.8 mm
Gap Width (s): 0.38 mm
Line Width (w): 2.9 mm

Power Divider Calculator

Port 2 Power 0.91 W
Port 3 Power 0.09 W
Dissipated Power 0.00 W

Note: For an ideal lossless coupler, total output power equals input power minus coupling loss. In practice, add ~0.1-0.5 dB for conductor and dielectric losses.

6 Lab Report Guidelines

Required Report Sections

1 Title Page: Course, date, student name, experiment title
2 Abstract: Brief summary of objectives and key findings (150 words)
3 Theory: Explain coupling mechanisms and S-parameters
4 Equipment List: Signal generator, spectrum analyzer, coupler specs
5 Procedure: Step-by-step measurement process
6 Results: Tables of measured vs. theoretical values
7 Graphs: Frequency response plots, Smith charts
8 Conclusion: Analysis of errors and bandwidth limitations

Data Tables

  • • Frequency vs. Coupling (dB)
  • • Frequency vs. Directivity
  • • Frequency vs. Return Loss
  • • Power distribution at center freq

Analysis Questions

  • • Why does directivity decrease with frequency?
  • • Calculate the coupling coefficient k from measurements
  • • Compare microstrip vs. waveguide couplers
  • • Design a 3dB quadrature hybrid

Grading Rubric

  • • Data accuracy (30%)
  • • Graph quality (20%)
  • • Theoretical analysis (25%)
  • • Conclusions (15%)
  • • Presentation (10%)

Submission: Submit PDF report via course portal. Include screenshots of simulation results and photos of actual measurements if hardware lab was performed. Due date: 1 week after lab session.