A 2.4 GHz Quarter-Wave Transformer on RO4350B

For an ideal 50 Ω source and a purely resistive 100 Ω load at 2.4 GHz, start with a 70.71 Ω transmission-line section that is 90° long. This article turns those circuit targets into an illustrative RO4350B microstrip seed, then calculates its off-center match. The result is a starting point for electromagnetic simulation, not production artwork or a measured response.

The RF layout foundation guide covers general layout practices. This worked example isolates one task: matching a specified real load at a specified reference plane. It also explains why an open-end correction does not belong on this through-connected transformer.

Define the load and reference planes

Assume the impedance looking into the load is 100 + j0 Ω at the end of the matching section. The source-side reference impedance is 50 Ω. These are hypothetical circuit requirements, not properties of RO4350B. Do not substitute a connector's nominal impedance or an antenna's DC resistance for the RF load impedance at this plane.

1. Input reference plane50 Ω system
2. Matching section70.71 Ω, 90° at 2.4 GHz
3. Load reference plane100 + j0 Ω

The ideal lossless quarter-wave relation is Z_in = Z_T² / R_L. Therefore Z_T = √(50 × 100) = 70.7107 Ω. A 50 Ω line that is simply made one-quarter wavelength long would instead transform 100 Ω to 25 Ω. Correct electrical length alone is not sufficient.

Altium's transformer design discussion distinguishes real-load matching from reactive-load matching. If the actual load contains appreciable reactance, first use a suitable network or line section to transform it to a real impedance, or synthesize a different match. Replacing a complex impedance with its magnitude does not solve that problem.

Convert impedance and phase to an initial microstrip geometry

For a transparent calculation, assume an air-covered microstrip over an infinite continuous ground, dielectric height h = 0.508 mm, relative permittivity εr = 3.66, and zero conductor thickness. Use the quasi-static Hammerstad–Jensen model documented by Qucs to solve width for 70.7107 Ω and obtain effective permittivity. No solder mask, roughness, dispersion, loss, nearby copper or discontinuities are included.

The Rogers RO4000 datasheet lists a design Dk of 3.66 for RO4350B using an 8–40 GHz differential-phase-length method. Here it is an illustrative constant input, not a certified 2.4 GHz value for this construction. Obtain an appropriate material model for the selected stackup before finalizing dimensions.

Calculate l = c / (4f√ε_eff) with c = 299,792,458 m/s and f = 2.4 × 10⁹ Hz. The free-space quarter wavelength is 31.2284 mm; using it directly would substantially overlengthen this microstrip. Extra digits make the calculation reproducible and are not a tolerance requirement.

Do not apply an open-end correction to a connected transformer

Both ends of this transformer connect to other conductors or loads. There is no free open termination at either end, so subtracting a generic open-stub extension from 18.9023 mm would model the wrong boundary condition. An actual open stub has fringing fields at its unterminated tip; its correction belongs to that stub's model.

The transformer still has junction effects. A width step, load pad, bend or launch can add parasitic fields and shift the best physical length. Include these structures in the EM model, define the port planes, and tune width and length together. Do not count a junction correction twice by including it both in a lumped element and in the meshed geometry.

Calculate a frequency sweep, not a universal bandwidth claim

For the same ideal line, set θ = (π/2)(f/2.4 GHz). Calculate Z_in = Z_T(R_Lcosθ + jZ_Tsinθ)/(Z_Tcosθ + jR_Lsinθ), then Γ = (Z_in − 50)/(Z_in + 50) and return loss = −20 log₁₀|Γ|. This sine/cosine form avoids the tangent singularity at 90°. Hold the 100 Ω load and line parameters constant throughout this demonstration.

The infinite center-frequency return loss is an ideal mathematical null, not an achievable test result. At 2.0 and 2.8 GHz the ideal calculation still exceeds 20 dB return loss. Thus the acceptable bandwidth depends on impedance ratio and the chosen match requirement; it cannot be assigned one universal percentage. These sample points do not qualify a real antenna, amplifier or modulated system across that band.

Turn the seed into a testable design

Replace zero thickness with the agreed finished copper profile, include mask coverage and the actual ground extent, and use material dispersion and loss appropriate to the band. Sweep width, dielectric height, Dk and length across justified limits. Check the actual load versus frequency and, for active devices, operating bias and power. A small-signal real-load example does not establish amplifier stability or large-signal efficiency.

Use the passive circuit specification workflow to set acceptance criteria. Review RF test planning before fabrication: define calibration and de-embedding planes, fixtures, the load model, and the frequency sweep. A conventional 50 Ω instrument port at the output is not the assumed 100 Ω termination; simulation and measurement must represent the same load.

Send a useful fabrication inquiry

Provide the frequency band, input reference impedance, load impedance data and its plane, proposed stackup, copper thickness, mask coverage, width and gap limits, board dimensions, quantity, and requested coupon or RF test scope. Identify dimensions the fabricator may adjust and require approval before those changes enter artwork.

Prepare the package on the RFQ page, then request a RO4350B PCB quotation from PCBSync. This example does not imply a price, lead time or manufacturing capability. RO4350B should be selected against the loss, stability and cost requirements; a quarter-wave section also becomes physically long at low frequencies, and this 2.4 GHz model is not a millimeter-wave qualification.