transmission lines is that the ground and signal conductors are on different physical planes. Coplanar waveguide (CPW), as the name implies, provides a coplanar structure of ground‐signal‐ground, as shown in Figure 1.30b. An alternative is grounded coplanar where the backside is a conductor as well, and in practice, all coplanar lines have associated package ground, but the ground may be ignored if there is a substantial air‐gap between the substrate and the package ground. The references provide some computations of coplanar waveguide impedance for various configurations (Wen 1969; Simons 2001). In microwave measurements, CPW is used extensively as a contacting means for on‐wafer measurements and is used to provide extremely low ground inductance for measuring microwave transistors and circuits, as shown in Figure 1.31, with either topside grounds (left) or backside grounds (right). Note that since the impedance depends only upon the scale of width to space, this allows contacts of large scale (such as probes) to be transitioned to small scale such as IC devices.
Figure 1.31 CPW‐mounted IC.
CPW has some inherent problems due to the ground being on a surface plane or sheet. In many instances the CPW line is mounted in a metal package, and the ground plane is grounded at the package wall. If the distance from the package wall to the ground plane edge approaches a quarter‐wavelength at the frequency of interest, or multiples thereof, then a transmission line mode can form such that the ground of the CPW appears as an open relative to the package ground. This concept of “hot grounds” for CPW has been observed in many situations and is sometimes avoided by periodically grounding one side to the other through a small cross connection on the backside of the CPW. Another method is to provide a lossy connection to the sidewall ground through absorptive material or thin film resist material to suppress energy in the unwanted mode. Another alternative is treating the CPW as a suspended substrate only under the gap between ground and conductor and “stitching” the CPW ground to the backside ground through a series of conductive vias. The impedance of these structures is lowered by the added ground, so an adjustment of the center line width is usually made to accommodate the additional ground paths.
1.8.3.4 Stripline
More common as a transmission line on an inner layer of a PC board, strip line consists of a thin strip or rectangle of metal sandwiched between two ground planes embedded in a uniform dielectric constant, as shown in Figure 1.30c. The impedance of these lines is much lower than the equivalent‐width microstrip line, but they have an advantage of being fully TEM in nature and so often the design of components such as coupled lines is easier as the even‐ and odd‐mode velocity factors are the same. An approximate formula for computing the value of a stripline impedance with a zero thickness strip is (Pozar 1990)
(1.88)
(1.89)
More complex formulas that include a broad range of applicability and include effects for finite strip thickness and asymmetric placement of the strip can be found in many references (IPC 2004; Cohn 1954).
1.9 Filters
Filters come in a variety of types including low pass, band pass, high pass, and band stop. Multiport filters form diplexers or multiplexers, which are used to separate or combine signals of different frequency from a common port to a port associated with the different frequencies of interest. Diplexers are sometimes called duplexers, but duplexing is a function of the operation of a communication system. That is, a system that can transmit and receive at the same time is said to operating in a duplex mode. A diplexer is used to support the duplex operation by keeping the transmit signal from saturating the receiver.
The structure and variety of filters are almost endless, but they all share these common attributes: low loss in the pass band, low reflection in the pass band, high reflection, and high loss in the stop band. In nearly every case, the goal of the design is to minimize unwanted loss, and this quality of a filter is often referred to as the Q of the filter. In microwave cases, filters are designed to operate into a matched impedance, so there is always loss associated with power from the source being absorbed by the load. The Q of a filter in operation is fixed by the loading of the ports and can never be infinite. The quality of a filter is usually defined by its unloaded Q, which accounts for the (desired) power loss from the source to the load.
For many filters, the desired qualities are a trade‐off between creating a maximally flat passband and creating a maximally sharp cutoff. Thus, the measurement of the transmission response of the filter is critical in evaluating the quality of a filter design. For most filters used in communications, the transmission responses is desired to be equally flat (rather than maximally flat) across the passband, resulting in filters that have Chevyshev‐type response (equal ripple) in the passband (Zverev 1967). The desire for sharp cutoffs has led to many filters employing an elliptic response, which provides for finite zeros in the transmission response. Stopband performance of high‐performance filters can also require careful consideration in measuring, with some requirements going beyond 130 dB of isolation over selected regions of the stop band. These extreme isolation requirements put tremendous burdens on the design of the filter, as well as the design and use of the measurement systems.
In modern communications systems using complex modulation, the phase response of the filters is also critical, and a significant design parameter is controlling the phase of the filter to follow a linear response, with a key measurement parameter being deviation from linear phase. Closely aligned to that is maintaining a constant group delay through the passband. Equalization techniques are utilized that can remove higher‐order phase responses, such that another measure of filter phase response is deviation from parabolic phase, where the phase is fitted to a second‐order response, and the deviation of the phase from this second‐order response is the measurement criteria. Some filters are used as part of a feed‐forward or matched system network where their phase response as well as absolute phase and delay must be carefully controlled.
The reflection response of filters is also a key measurement parameter. To the first order, any signal that is reflected is not transmitted so that high reflections lead to high transmission loss. However, the loss due to reflection for most well‐matched filters is much less than the dissipation loss. Still, low reflections at the test ports are required to avoid excess transmission ripple from concatenated components, and even moderate reflections from filters in a high‐power transmission path can cause damage to the preceding power amplifier. Thus, very low return loss is often a critical parameter of filters and also a difficult parameter to measure well. This becomes especially true in the case of diplex and multiplex filters, where the loading of any port affects the return loss of the common port.
For high‐power applications, the filter itself can become a source of IM distortion, and the attribute passive inter‐modulation (PIM) has become common in the measurement of these high‐power filters. Poor mechanical contacts between components in a filter, poor plating on a filter, or the use of magnetic materials in the plating or construction of the filter can lead to hysteresis effects that cause IMD to be created in an otherwise passive structure. The level of IMD typically found in these filters is less than −155 dBc, but this can be a difficult spec to meet without careful design and assembly.
Most of these high‐performance communication filters are designed using coupled‐resonator
