4.2: Measurement of Scattering Parameters

\(S\) parameters are measured using a network analyzer called an automatic network analyzer (ANA), or more commonly a vector network analyzer (VNA).

4.2.1 Vector Network Analyzer

The VNA is based on separating the forward- and backward-traveling voltage waves using a directional coupler. The separated traveling waves are then the total voltages on the coupled lines of the directional coupler. They are down-converted to perhaps \(100\text{ kHz}\) and then sampled by an analog-to-digital converter [1]. Schematics of modern VNAs are shown in Figures \(\PageIndex{1}\) and \(\PageIndex{2}\) and comprise

1. A frequency synthesizer for stable generation of a sinewave.
2. A display plotting the \(S\) parameters in various forms, with a Smith chart being most commonly used.
3. An \(S\) parameter test set. This device generally has two measuring ports so that when required \(S_{11},\: S_{12},\: S_{21},\) and \(S_{22}\) can all be determined under program control. The main components are switches and directional couplers. Directional couplers separate the forward- and backward-traveling wave components. Network analyzers with more than two ports—four-port network analyzers are popular—have more switches and directional couplers. The mixers map the amplitude and phase of the RF signal to the IF, commonly around \(100\text{ kHz}\), which is sampled by the ADC.
4. A computer controller used in correcting errors and converting the results to the desired form.

For RF measurements up to a few tens of gigahertz, most of these functions are incorporated in a single instrument. At higher frequencies and with older equipment multiple units are used. An outline of such a system is shown in Figure \(\PageIndex{3}\)(a) and a photograph in Figure \(\PageIndex{3}\)(c). In the foreground of Figure \(\PageIndex{3}\)(c) is a probe station that has a stage for an IC or RF circuit board and mounts for micropositioners to which microprobes are attached. The vertical tube-shaped object is a microscope-mounted camera.

The probes are mounted on micromanipulators such as those shown in Figure \(\PageIndex{4}\). These provide precision positioning with \(x-y-z\) movement and an axis rotation to accommodate probing on substrates that are not completely flat.

Figure \(\PageIndex{1}\): Switch-based vector network analyzer system with two receivers. The directional couplers selectively couple forward- or backward-traveling waves. With the directional coupler (see inset), a traveling wave inserted at Port \(\mathsf{2}\) appears only at Port \(\mathsf{1}\). A traveling wave inserted at Port \(\mathsf{1}\) appears at Port \(\mathsf{2}\) and a coupled version at Port \(\mathsf{3}\). A traveling wave inserted at Port \(\mathsf{3}\) appears only at Port \(\mathsf{1}\). Switch positions determine which \(S\) parameter is measured.

Figure \(\PageIndex{2}\): Vector network analyzer system with four receivers.

Figure \(\PageIndex{3}\): \(S\) parameter measurement system: (a) shown in a configuration to do on-chip testing; (b) details of coplanar probes with a GSG configuration and contacting pads; and (c) a vector network analyzer in the background with probe station including camera.

Figure \(\PageIndex{4}\): Micropositioners used with coplanar probes. Used with permission of J MicroTechnology, Inc.

Probing elements required for on-wafer measurements are shown in Figure \(\PageIndex{5}\). Figure \(\PageIndex{5}\)(a) shows a single RF probe that is essentially an extended coaxial line. Figure \(\PageIndex{5}\)(c) shows a microprobe making a connection to a transmission line on an IC and the lower image in Figure \(\PageIndex{5}\)(b) shows greater detail of the contact area.

A typical microprobe is based on a micro coaxial cable with the center conductor (carrying the signal) extended a millimeter or so to form a needlelike contact. Two other needle-like contacts are made by attaching short extensions to the outer conductor of the coaxial line on either side of the signal connection (see the top image in Figure \(\PageIndex{5}\)(b)). Such probes are called

Figure \(\PageIndex{5}\): RF probes: (a) single RF probe probe; (b) detail of a GSG probe and contacting an IC; (c) an IC under test; (d) layout of a calibration substrate used with GSG probes; (e) probes contacting a through CPW structure on the calibration substrate; and (f) a probe card with 2 RF probes (top and bottom) and \(13\) needle probes for DC and low-frequency connections. ((a), (b) top, (d), (e), (f) Copyright GGB Industries Inc., used with permission [2].)

Figure \(\PageIndex{6}\): Use of a CPW-to-microstrip adaptor enabling coplanar probes to be used in characterizing a non-CPW device. The adaptors provide a low insertion loss CPW-to-microstrip transition. Used with permission of J microTechnology, Inc.

ground-signal-ground (GSG) probes and transition from a coaxial cable to an on-wafer CPW line, providing a smooth transition of the EM fields from those of a coaxial line to those of the CPW line. The on-wafer pads can be as small as \(50\:\mu\text{m}\) on a side.

Measurement using CPW probes and manipulators enables repeatable measurements to be made from DC to above \(100\text{ GHz}\). Such measurements require repeatability of probe connections that are better than \(1\:\mu\text{m}\). When the DUT has microstrip connections, it is necessary to use a CPW-to-microstrip adapter, as shown in Figure \(\PageIndex{6}\). The layout of a suitable adapter is shown in Figure \(\PageIndex{6}\)(a). In Figure \(\PageIndex{6}\)(c and d) two adaptors are shown in use in the characterization of a microwave transistor. GSG probes contact the adapters and the grounds are connected to the backside metalization by vias. Calibration uses the microstrip transmission line calibration substrates shown in Figure \(\PageIndex{6}\)(b).