ROG Blog

The Rog Blog is contributed by John Coonrod and various other experts from Rogers Corporation, providing technical advice and information about RF/microwave materials.

Taming Discontinuities in Microwave Circuits

July 7, 2014

Designing high-frequency microwave circuits and, with increasing frequency, millimeter-wave frequencies require for the most part laying out carefully conceived transmission lines to carry those high-frequency signals across a printed-circuit board (PCB). Of course, if the task of fabricating the PCB was simply a matter of adding circuit elements, such as resistors, capacitors, and inductors, to create the necessary frequency-domain/time-domain response for the PCB, it might go somewhat easier. But every PCB with high-frequency transmission lines must also manage any number of circuit discontinuities and junctions as part of that design—these are those locations where signals must pass some change in the transmission-line path, such as a transition in the width of a transmission line, a gap between sections of transmission line, even an abrupt change in direction for the transmission line. In all cases, a high-frequency signal that has been propagating along a straight and consistent transmission line must now navigate some form of obstruction, such as an abrupt change in direction, a difference in transmission-line width, or a gap in the transmission line path. Since these and similar discontinuities can be found on all but the simplest of RF/microwave circuits, the question is “How can the effects of these discontinuities be minimized through the thoughtful choice of PCB material?”

Using a microstrip transmission line as an example that most microwave engineers understand, this circuit configuration is comprised of RLGC properties. A simple representation of these properties as they relate to microstrip-transmission-line features is shown in Fig. 1.

Fig 1

As can be seen, an alteration of the signal conductor will cause changes in inductance and the capacitance is affected by a change in the cross-section area between the signal conductor and the ground plane below. The simple circuit drawing is meant to represent the RLGC attributes of a microstrip transmission line. Another way to think of this is by using these properties as an infinitesimal piece of transmission line with unit-per-length representations of the circuit elements as shown in Fig. 2.

Fig 2

A change in conductor width of the transmission line will impact the RLGC configuration in the area of the circuit with the change. Some common changes to a microstrip transmission line, also known as discontinuities, are shown in Fig. 3 with their associated RLGC impacts.  

Fig 3

The 90° bend is actually a change in the cross-sectional conductor area in the region of the bend between T1 and T2. The change in area is easiest to picture if a diagonal line is drawn from the inside corner to the outside corner of the bend and just that area is considered.

The middle section of Fig. 3 shows a gap in the transmission line, often used to adjust coupling for certain microwave circuit functions. The slit in the transmission line shown in the right-hand circuit of Fig. 3 is often used in tuning filters or for mode velocity adjustments in couplers.

The differences in the RLGC circuit influences for the discontinuities can also be related to complex impedance. The impedance values of the discontinuities have normal variations due to the process of circuit fabrication and the materials used. 

How can the choice of PCB material ease the effects of circuit discontinuities and junctions? Consistency is vital for a material, so that it will perform as expected, according to CAE simulations and according to the real world. Because a discontinuity will introduce a shift in impedance, it is hoped that the PCB substrate will provide the most stable basis for a circuit design’s target impedance, usually 50 ?, as possible. But certain attributes can impact a PCB’s impedance consistency and predictability.

The thickness tolerance of a high-frequency circuit material might be its most significant variable when trying to achieve consistent, repeatable impedance. Even slight variations in the thickness of a PCB material represents a difference in the effective dielectric constant for a microstrip transmission line, and a variation in the impedance of the circuit from its nominal value. Although the changes in impedance from discontinuities and junctions are to be expected, and should be included in any CAE model for a design, the variations in the thickness of the PCB material are typically not accounted for as a cause of variations in impedance. Circuit materials are generally offered in a variety of thicknesses, with different thickness tolerances as a function of thickness.

Another key material characteristic impacting a circuit’s impedance (with or without discontinuities) is the PCB material’s dielectric constant (Dk). Not only does every high-frequency PCB material have a Dk value relative to the unity of a vacuum, but the nominal Dk value also has a tolerance and some materials are much better controlled for Dk than others.

As an example, RO3003™ laminates from Rogers Corp. ( are ceramic-filled polytetrafluoroethylene (PTFE) materials engineered for a Dk value of 3.00 at 10 GHz in the z-direction. The material is specified for a remarkable Dk tolerance with ±0.04 across a circuit board, so that impedance variations due to changes in dielectric constant will be at a minimum with this material. The material also maintains stable dielectric constant with temperature, as measured by its low thermal coefficient of dielectric constant (TCDk) of 13 ppm/°C at 10 GHz for temperatures from 0 to +100°C. By ensuring that a PCB material maintains consistent Dk across the material and across a temperature range of interest, essentially one more design variable can be eliminated—variations in impedance due to variations in a circuit substrate’s Dk value—when designing and fabricating high-frequency circuits.

To examine another example, RO4350B™ laminates from Rogers Corp. are reinforced hydrocarbon/ceramic laminate materials with dielectric constant of 3.48 at 10 GHz and room temperature. Like RO3003 laminates, they are manufactured to an extremely tight thickness tolerance, which contributes to maintaining tightly controlled impedances for transmission lines and circuit structures. Like the RO3003 material, RO4350B material delivers outstanding Dk tolerance across a circuit board to tightly control the impedance of transmission lines and other circuit structures. The Dk tolerance remains within ±0.05 across the circuit board or multiple circuit boards when measured at 10 GHz. The TCDk is somewhat higher than that of RO3003 material, at 50 ppm/°C at 10 GHz, but still acceptable for a variety of designs.

Of course, achieving and maintaining consistent impedance for any PCB in large part depends on the precision and repeatability of the circuit-fabrication process, and reliable circuit fabrication techniques are needed for predictable results in terms of maintaining consistent impedance. But choosing a PCB material with tightly controlled thickness and tightly controlled dielectric constant can support consistent impedance across a circuit board, and make it more straightforward to model all the discontinuities and junctions that might be found in a high-frequency circuit.

Do you have a design or fabrication question? John Coonrod and Joe Davis are available to help. Log in to the Rogers Technology Support Hub and “Ask an Engineer” today.

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