The wireless industry is demanding modules with more functionality and smaller size¹. The designer must achieve this combined functionality at a lower cost, footprint and height, than the separate packaged units. This leads to inventing or rediscovering creative methods of decreasing circuit sizes using both old and new technologies.

This article details a shortwave coupler design briefly described in previous literature². While this is not a new concept, it is a relatively obscure and unsubstantiated approach to solving this new market challenge.

The main focus is the design and fabrication of shortwave couplers. The design was primarily driven by a desire for cost reductions. The couplers have to meet the dictated performance without increasing the overall power amplifier (PA) module size.

Earlier coupler design consisted of a buried transmission line beneath the output amplifier matching circuitry. This design lacked the required directivity and incurred an additional cost due to the multilayer substrate requirements. The module size requirements would not allow for a full quarter wave edge coupled transmission line coupler.

The current design was able to reduce the module cost by providing a shortwave edge coupled microstrip coupler design in a two layer substrate construction. In addition, this design exceeded the 10 dB directivity requirement. Some of the cost factors in SiP module fabrication are given in figure 1.

There are many coupler topologies available to designers. The most common is two transmission lines separated by a constant gap with a length of a quarter wavelength at the frequency of operation. The most simplistic coupler consists of one capacitor. This design is plagued with a large variation in the coupling coefficient and no directivity. It can be used, however, when an isolator or circulator follows the capacitor (see figure 2).

The quarter wavelength coupler is the most common type at higher frequencies when directivity is desired. These couplers require a large amount of board real estate. At lower frequencies, a lumped element approach is more common. This approach can be used up to frequencies in the low gigahertz range. The discrete component values become too small at frequencies beyond two gigahertz. The lumped element approach may be smaller than the quarter wavelength coupler depending on the frequency of operation. However, it is more costly.

Several lumped circuit topologies are shown in figure 3. These topologies contain eight or nine components. The directivity provided by quarter wavelength couplers is limited to typically only 20 dB over any appreciable bandwidth. A method to improve the directivity with capacitor terminations at both ends has been documented⁴. The capacitor terminations effect only the odd mode excitation (see figure 4). The capacitor value can be determined to make the even and odd mode phase velocity the same at a particular frequency⁵. The isolation is perfect when the phase velocities are equal (see equation 32).

The lumped capacitor terminations drastically improve the quarter wavelength coupler. Could they also improve a short wavelength coupler with poor directivity to the same typical 20 dB directivity of a full quarter wavelength coupler? This was investigated with a single capacitor termination to meet a 10 dB directivity requirement. The capacitor allowed for the coupled lines to be shorter while the combination can provide the same directivity as quarter wave coupled lines.

However, as we all are quite aware of, there is no such thing as a free lunch. The directivity with this approach varies more than the directivity of the quarter wave coupled line approach. The coupling coefficient, however, exhibits similar variations as the quarter wave coupled line approach.

The initial interdigitated capacitor shortwave coupler design is depicted in figure 5. A similar design was fabricated with a discrete capacitor. These initial prototype units were fabricated on a lossy 0.4 mm thick BT dielectric material. This design required 10 dB of directivity in both the global system for mobile communications (GSM) and digital cellular systems (DCS) bands. The desired coupling factor was 20 dB for GSM and 15 dB for DCS. The measured coupler required an extra tapered line to mount an SMA connector for measurement (see figure 6). The measurements did not included a correction factor for the extra tapered line length.

The measured insertion loss agrees well with the method of moments (MOM) simulation (see figure 7). Additionally, the return loss compares favorably as well.

The coupling coefficient exhibits a slight, 2 dB shift. The measured results indicate tighter coupling (20.4 dB simulated at 900 MHz versus 18.4 dB measured and 15.2 dB simulated at 1750 MHz versus 12.9 dB measured).

Although the measured directivity meets the 10 dB requirement, it is significantly different than the simulation. The yield data in figure 8 and 9 show that directivity has the largest variation. The yield data, however, was simulated with a linear model for the coupler. The linear and MOM data diverge in return loss and insertion loss. This can be deferred by the insertion loss and return losses at the peak of the histograms in figures 8 and 9 versus the MOM simulation results in figure 7.

The coupling coefficient is in close agreement between the MOM and linear simulation while the directivity is slightly shifted. The overall directivity response versus frequency, however, is similar between the linear and MOM simulations.

The improved shortwave coupler is depicted in figure 10. This design significantly improved the insertion loss. It is also physically smaller than the previous coupler. This improvement was made by increasing the conductor width and making the gap more narrow. However, the directivity of this coupler is more susceptible to gap variations. In addition, designs were fabricated using this approach with much higher directivity. A directivity of 45 dB is possible, however, finer geometry is needed. This increases the variation due to processing tolerance. The 45 dB directivity coupler experiences a worst case directivity of 25 dB over the range of process tolerances.

A four port network symmetric about the plane P, P' is depicted in figure 11. The general four port S-parameters can be reduced by the symmetry to⁴:

Where:

and:

The symmetrical four port is excited with two equal magnitude and in-phase sources, even mode excitation, in figure 12. Under this excitation, the incident and reflected voltages can be written in terms of the S-parameter matrix in equation 1 as:

This can easily be rewritten as:

Where:

The symmetrical four port is excited with two equal magnitude sources that differ in phase by 180°, odd mode excitation, in figure 13. Under this excitation, the incident and reflected voltages can be written in terms of the S-parameter matrix in equation 1 as:

This can easily be rewritten as:

Where:

Using equations 6 and 9, the scattering matrices [S_A] and [S_B] are:

and:

All of the S-parameters for the symmetric four port can now be written in terms of these even and odd order S-parameters. Using equations 1, 10 and 11, the symmetric four port S-parameters are:

and:

There are two ways to satisfy a perfectly matched condition, S₁₁ = S₂₂ = S₃₃ = S₄₄ = 0. The first case, S_11e = S_11o = S_22e = S_22o = 0, results in a forward coupler. The second case will be investigated further. Setting equation 12 and 16 equal to zero without any of the terms in these equations equal to zero yields;

and:

The perfect isolation on port four is achieved when S₄₁ = 0. Using equation 15, this results in:

These conditions result in a backward wave coupler. This coupler has maximum performance, insertion loss and directivity, for a length equal to a quarter wavelength at the frequency of operation. The coupled port and the output port will differ in phase by 90°. The equivalent circuits for the even and odd modes are given in figure 14. The ABCD matrix for a lossless, γ = jβ, transmission line circuit with a Z_o characteristic impedance and length ι is:

Using equation 21, the ABCD matrices for the even and odd modes of the coupler are:

and:

The input reflection coefficient for a match terminated ABCD network with a characteristic impedance of Z_o is:

The output port reflection coefficient for a match terminated ABCD network with a characteristic impedance of Z_o is:

The transmission coefficient between the input and output ports is:

Using equations 22, 23, 24 and 25, the even and odd mode reflection coefficients are:

and:

Under ideal conditions, the propagation velocity is the same for even and odd mode excitation. Setting β₀ = β_e = β and the condition that S_11e = -S_11o results in:

The ideal even and odd mode transmission scattering parameters are found using equations 22, 23 and 26. These are:

and:

Note that the condition S_21e = S_21o is met when equation 29 is valid and the phase velocities are equal, β₀ = β_e = β. The isolation under these conditions is:

The shortwave coupler was shown to provide good directivity in a small size. A discrete or interdigitated capacitor could be used. Results were shown with an interdigitated approach for reduced cost. The designs that were shown exceeded the 10 dB directivity requirement including circuit fabrication tolerances.

1. A. Pentchev, P. Swinkels, and G. Paola, “Concepts and Implementation of a GSM PA/front-end Module,” RF Design, October 2001, pp. 26-35.

2. P. Vizmuller, RF Design Guide Systems, Circuits, and Equations, (Boston: Artech House, 1995)

3. S. Erst, Electronics Equations Handbook, (New York: McGraw-Hill, 1989).

4. R. Mongia, I. Bahl, and P. Bhartia, RF and Microwave Coupled line Circuits, (Boston: Artech House, 1999).

5. D. Kajfez, “Raise Coupler Directivity with Lumped Compensation,” Microwaves, March 1978, pp. 64-70.

Michael P. Gaynor is a technical director for Amkor Technology Inc's (www.amkor.com) RF Design and Applications Group. He is responsible for RF circuit and system architecture design mainly in system in package (SiP) solutions. Mike joined Amkor in July 2000. He has 16 years of experience in RF/microwave product development with an emphasis on transmitter linearization. His design experience includes base station power amplifiers, portable phone architecture and circuit design, and modules spanning DC to 32 GHz. Mike received his B.S.E.E. from the Illinois Institute of Technology (IIT) in 1986 and his M.S.E.E. from IIT in 1993 with concentration in areas of communications and RF and microwave design. He is a member of the IEEE and its Microwave Theory and Techniques Society, Eta Kappa Nu and Tau Beta Pi. He can be contacted at mgayn@amkor.com.