How do I calculate the coupling factor, directivity, and isolation of a directional coupler?
Coupler Specifications
Understanding coupling, directivity, and isolation is essential for selecting and specifying directional couplers for power monitoring, VSWR measurement, and signal sampling applications.
Measurement of Coupler Parameters
(1) Coupling measurement: connect VNA Port 1 to the input (Port 1 of the coupler). Connect VNA Port 2 to the coupled port (Port 3). Terminate the through port (Port 2) and isolated port (Port 4) in 50 ohms. Measure S31 (or S13). Coupling = -20×log10(|S31|) = |S31| in dB (positive number). (2) Isolation measurement: connect VNA Port 1 to the input (Port 1). Connect VNA Port 2 to the isolated port (Port 4). Terminate the through port (Port 2) and coupled port (Port 3) in 50 ohms. Measure S41. Isolation = -20×log10(|S41|). (3) Directivity: calculated from coupling and isolation: D = I - C. Or directly measured: connect VNA Port 1 to the through port (Port 2). Connect VNA Port 2 to the coupled port (Port 3). Terminate Port 1 (input) and Port 4 (isolated) in 50 ohms. Measure S32. Directivity = Coupling - |S32| (dB). This measures the coupler response to a signal traveling in the reverse direction through the main line. (4) Through-path loss: measure S21 (Port 1 to Port 2). Through IL = |S21| in dB. For a lossless coupler: IL = -10×log10(1 - 10^(-C/10)). The difference between the measured and theoretical IL is the excess (dissipative) loss.
Directivity Importance
Directivity determines the accuracy of power and VSWR measurements using the coupler: (1) Forward power monitoring: the coupled port reading represents forward power. Any reverse power leaking to the coupled port (due to finite directivity) corrupts the reading. The error: delta_P = ±20×log10(1 ± |Gamma_load| × 10^(-D/20)). For a load with VSWR = 2.0 (|Gamma| = 0.33) and coupler D = 20 dB: delta_P = ±20×log10(1 ± 0.33 × 0.1) = ±20×log10(1 ± 0.033) = ±0.29 dB. For D = 30 dB: delta_P = ±20×log10(1 ± 0.033 × 0.032) = ±0.01 dB (negligible). (2) Return loss measurement: using the coupler to measure the reflected power from the load. The directivity limits the minimum measurable return loss: if D = 20 dB, the coupler cannot distinguish a real reflection of -20 dB from the directivity leakage. Practical limit: measurable RL < D - 6 dB (for approximately ±1 dB accuracy). For D = 30 dB: can measure RL up to 24 dB accurately. For VNA-quality measurements (RL up to 40 dB): need D > 46 dB.
Frequency Dependence
Coupler parameters vary with frequency: (1) Coupling: relatively flat across the design bandwidth for multi-hole and multi-section couplers. For a single-section coupled-line coupler (quarter-wave): coupling is strongest at the design frequency and decreases at band edges. Coupling flatness: ±0.5-1 dB across the bandwidth for a well-designed coupler. (2) Directivity: tends to be best at the design frequency and degrades at band edges. For a microstrip coupled-line coupler: D can be 15 dB at center frequency and drop to 10 dB at band edges. Design techniques for high directivity: use odd/even mode velocity equalization (achieved by using tandem connections, capacitive compensation, or multilayer structures). (3) Isolation: since I = C + D, isolation tracks the sum of coupling and directivity variations. If coupling is flat but directivity degrades at band edges: isolation degrades at band edges.
I = -10log₁₀(P_isolated/P_in) dB
D = I - C dB
Error: δP = ±20log₁₀(1 ± |Γ|·10^(-D/20))
Through IL = -10log₁₀(1 - 10^(-C/10))
Frequently Asked Questions
Why is microstrip coupler directivity limited to 15-20 dB?
Microstrip coupled-line couplers have an inherent directivity limitation caused by the unequal even-mode and odd-mode phase velocities. In microstrip: the even mode (both lines excited with the same polarity) has a higher effective dielectric constant (more field in the substrate) than the odd mode (lines excited with opposite polarity, more field in the air). This velocity difference means the even and odd mode signals do not cancel perfectly at the isolated port, limiting the directivity to 15-20 dB. Solutions: (1) Use stripline (symmetric, equal velocities, D > 30 dB). (2) Add capacitive compensation (lumped capacitors at the coupled-line ends to equalize velocities). (3) Use a Podell-type compensated microstrip coupler (adding a capacitor at the midpoint of the coupled lines). (4) Use a multi-section Tandem coupler (two cascaded couplers with specific phase relationships that cancel the directivity error).
What coupling value should I choose for power monitoring?
The coupling value depends on the power level you are monitoring and the sensitivity of your detector: for high-power transmitters (10-1000W): use -30 to -40 dB coupling. At 100W (+50 dBm) input: -30 dB coupling gives +20 dBm at the coupled port (adequate for most detectors). -40 dB coupling gives +10 dBm. For medium-power (0.1-10W): use -20 to -30 dB coupling. At 1W (+30 dBm): -20 dB gives +10 dBm. For low-power signals (< 0.1W): use -10 to -20 dB coupling. At 10 mW (+10 dBm): -10 dB gives 0 dBm. Consider: (a) The coupled port power should be within the detector dynamic range (-30 to +20 dBm for most detectors). (b) Higher coupling = more main-line insertion loss. Choose the weakest coupling that provides sufficient coupled-port power.
How do I measure directivity accurately?
Directivity measurement requires high dynamic range because the isolated port signal is very weak (C + D dB below the input). Steps: (1) Connect VNA Port 1 to the coupler through port (Port 2), VNA Port 2 to the coupled port (Port 3). (2) Terminate Port 1 (input) and Port 4 (isolated) in precision 50-ohm loads. (3) Measure S32. This is the signal coupled in the reverse direction (leakage). (4) Directivity = Coupling - |S32|. If coupling = 20 dB and S32 = -45 dB: D = 45 - 20 = 25 dB. Challenge: the load terminations must be perfect. A load with 40 dB return loss reflects a signal that is only 40 dB below the input, which may be comparable to the directivity leakage. Use precision loads (RL > 50 dB) or correct for the load RL.