Introduction

Stripline couplers are essential components in RF and microwave circuits that allow designers to split RF power between two lines at desired proportions. These four-port devices operate on the principle of electromagnetic coupling and are widely used in signal routing, power division, and signal sampling applications across various frequency ranges. This article explores the design equations and principles for two common types of stripline couplers: broadside and edgewise configurations.

Basic Principles of Stripline Couplers

A stripline coupler typically consists of two parallel transmission lines with equal widths positioned at equal distances from ground planes. The coupling region spans a quarter-wavelength at the design frequency, creating a predictable power division between the output ports. In a standard four-port coupler, ports 1 and 2 are located on the driven line, while ports 3 and 4 are on the coupled line. Port 3 is adjacent to port 2, and port 4 is adjacent to port 1.

The coupling coefficient, measured in decibels (dB), expresses the power ratio between port 4 and port 1. A lower positive dB value indicates stronger coupling. For instance, a 3 dB coupling coefficient represents an approximately equal power split between ports 2 and 4, while a 10 dB coefficient indicates a 9:1 power division ratio.

Broadside vs. Edgewise Configurations

Broadside Stripline Couplers

Broadside couplers are typically constructed using three circuit boards forming two signal layers between ground planes. This configuration is preferred for applications requiring high coupling coefficients (lower dB values) due to its ability to achieve tight coupling between the lines.

The broadside configuration places the coupled lines directly above and below each other, separated by a dielectric material. This arrangement maximizes the coupling area between the lines, allowing for coupling coefficients as low as 1-3 dB to be achieved relatively easily.

Edgewise Stripline Couplers

Edgewise couplers, on the other hand, require only two boards with a single signal layer. In this configuration, the coupled lines are positioned side by side on the same plane. This arrangement is typically used for applications requiring lower coupling (higher dB values), commonly in the range of 8-20 dB.

The edgewise configuration simplifies the manufacturing process compared to broadside couplers but limits the achievable coupling coefficient due to the reduced coupling area between the lines.

Read more about:

• Rogers 3003
• Rogers 4003c
• Rogers 5880
• Rogers 4350B

Design Equations and Parameters

Both broadside and edgewise couplers share certain fundamental relationships between their design parameters. The key parameters include:

• D: Coupling coefficient in dB
• Z₀: Overall characteristic impedance in ohms
• V: Voltage ratio (V = e^(D/-8.68589))
• Z₀,even and Z₀,odd: Even and odd mode impedances

Common relationships include:

• Z₀ = √(Z₀,even × Z₀,odd)
• D = -8.68589 × log₍ₑ₎((Z₀,even – Z₀,odd)/(Z₀,even + Z₀,odd))
• Z₀,even/Z₀,odd = (1 + V)/(1 – V)

Broadside Coupler Design Equations

For broadside couplers, the design parameters are expressed as ratios of line spacing and width to the total ground plane spacing:

• s: Ratio of line spacing to ground plane spacing
• w: Ratio of line width to ground plane spacing
• εᵣ: Relative permittivity of the dielectric material

Key equations include:

• Z₀,odd = 296.1s/(εᵣ × tanh⁻¹(k))
• Z₀,even = 188.3 × K(k’)/[εᵣ × K(k)]
• w = (π/2) × [tanh⁻¹(R) – s × tanh⁻¹(R/k)]

Where:

• k’ = 1 – k²
• R = (k – s)/(1 – s×k)
• K(k) represents the elliptic integral of the first kind with modulus k

Edgewise Coupler Design Equations

For edgewise couplers, the design parameters are expressed as absolute dimensional values:

• w: Width of the lines
• s: Spacing between the lines
• b: Ground plane spacing

Key equations include:

• kₑᵥₑₙ = tanh((π×w)/(2×b)) × tanh((π×(w+s))/(2×b))
• k’ₑᵥₑₙ = 1 – k²ₑᵥₑₙ
• kₒₐₐ = tanh((π×w)/(2×b)) × coth((π×(w+s))/(2×b))
• k’ₒₐₐ = 1 – k²ₒₐₐ
• Z₀,even = (30π/√εᵣ) × [K(k’ₑᵥₑₙ)/K(kₑᵥₑₙ)]
• Z₀,odd = (30π/√εᵣ) × [K(k’ₒₐₐ)/K(kₒₐₐ)]

Where:

• tanh(i) is the hyperbolic tangent of i
• coth(i) is the hyperbolic cotangent of i (1/tanh(i))

Design Considerations and Assumptions

When designing stripline couplers using these equations, several assumptions are made:

1. The thickness of the conductors is considered negligible
2. The coupled lines have equal width
3. Distance to ground planes on either side of the coupled lines is equal
4. Dielectric material completely fills the space between ground planes not occupied by conductor
5. All layers of dielectric material have the same relative permittivity (εᵣ)

Practical Examples

Broadside Coupler Examples

For a broadside coupler using RT/duroid 5880 substrate:

• Outer board thickness: 0.031 inches
• Center board thickness: 0.005 inches
• Line width: 0.200 inches
• Resulting coupling coefficient: 1.47 dB
• Characteristic impedance: 9.83 ohms

For a broadside coupler using TMM-10 substrate:

• Outer board thickness: 0.050 inches
• Center board thickness: 0.015 inches
• Line width: 0.175 inches
• Resulting coupling coefficient: 2.82 dB
• Characteristic impedance: 10.68 ohms

Edgewise Coupler Examples

For an edgewise coupler using RT/duroid 5880 substrate:

• Board thickness: 0.031 inches
• Line spacing: 0.005 inches
• Line width: 0.025 inches
• Resulting coupling coefficient: 9.74 dB
• Characteristic impedance: 68.53 ohms

For an edgewise coupler using TMM-10 substrate:

• Board thickness: 0.025 inches
• Line spacing: 0.005 inches
• Line width: 0.010 inches
• Resulting coupling coefficient: 8.89 dB
• Characteristic impedance: 46.10 ohms

Applications and Selection Criteria

The choice between broadside and edgewise couplers depends on several factors:

1. Required Coupling Coefficient: Broadside couplers are preferred for tight coupling (1-6 dB), while edgewise couplers are suitable for looser coupling (7-20 dB).
2. Manufacturing Complexity: Edgewise couplers are generally simpler to manufacture as they require only a single signal layer.
3. Space Constraints: Edgewise couplers typically require more lateral space but less vertical space compared to broadside couplers.
4. Frequency Range: Both types can operate across a wide frequency range, but the bandwidth characteristics may differ.
5. Impedance Requirements: The desired system impedance (typically 50 or 75 ohms) will influence the selection of line width, spacing, and substrate material.

Conclusion

Stripline couplers in both broadside and edgewise configurations offer designers flexible solutions for power division and signal sampling in RF and microwave circuits. The design equations provided in this article allow for accurate prediction of coupling coefficients and impedance matching, enabling optimized performance for specific applications.

While broadside couplers excel in achieving tight coupling with values as low as 1-3 dB, edgewise couplers offer simpler construction and are ideal for applications requiring coupling in the range of 8-20 dB. The choice between these configurations depends on the specific requirements of the application, including coupling strength, manufacturing complexity, space constraints, and operating frequency range.

By understanding the fundamental principles and design equations presented here, engineers can effectively design stripline couplers tailored to their specific system requirements.