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Characterization of microwave networks requires distinguishing between forward and reverse traveling waves. Unfortunately, no directional device is perfect, which can lead to large measurement errors. In this note, we show that the measurement of return loss and standing wave ratio is complicated by the limited performance of the directional devices used to measure reflected power. Explicit expressions for the measurement errors as a function of directivity, return loss, and reflected phase are derived. The only accurate and convenient way to measure return loss is to use a well-matched, highly directive directional coupler or bridge. Standing
Wave Ratio and Return Loss
A key performance metric for any microwave or RF network is how well the load impedance is matched to the source impedance. This match determines how much power can be delivered and how much will be reflected back to the transmitter, measured by return loss, or the ratio of reflected power to transmitted power. Traditionally, this quality of a component has been described using the voltage standing wave ratio (VSWR), or the ratio of the maximum to minimum voltage of a standing wave on the line before the component, because this quantity was easier to measure than return loss before the availability of network analyzers. These two parameters answer the same question: How much power is output from the device under test (DUT), and how much power is reflected?
To measure the power reflected from the DUT, a directional device that can distinguish between forward and reverse traveling waves is needed. One such directional device is the directional coupler (Figure 1). A directional coupler is a four-port device that samples the signal running through the line, but in a way that distinguishes between forward and reverse traveling waves. To measure the power reflected from the DUT, a directional device that can distinguish between forward and reverse traveling waves is needed. One such directional device is the directional coupler (Figure 1). A directional coupler is a four-port device that samples the signal running through the line, but in a way that distinguishes between forward and reverse traveling waves.
Figure 1: Schematic diagram of a directional coupler.
In this device, the input signal is partially split between the output port and the coupled port, and no signal appears at isolated port 2. The isolation that exists between port 1 and port 4 is caused by the destructive interference of odd- and even-mode internal reflections at the isolated port; the constructive interference of these modes also produces a coupled signal. Couplers are reciprocal circuits, which means that waves propagating in the opposite direction will be sampled at port 4 (the forward isolated port) and isolated at port 2 (the forward coupled port). In practice, the goal of the coupler designer is to obtain as much isolation as possible between the input and isolated ports.
The value that defines the coupler's ability to distinguish between forward and reverse waves is called directivity. Directivity is positively defined as
Where D is directivity, S31 is coupling ratio, S21 is insertion loss, S32 is isolation, and all terms are defined in dB. Note that most datasheets use this definition
Insertion loss is not included. Since this definition does not include insertion loss, it is not as meaningful as the merit value of echo power measurement. However, (2) is valid when discussing forward power measurements and is commonly used by the industry. The following example illustrates the importance of directivity. Suppose we want to measure the power on a transmission line terminated by an unknown impedance (Figure 2). Using a coupler, we can couple off some of the power (e.g. 1%) and measure it using a detector. If the DUT impedance is perfectly matched to the transmission line, no reflections will occur (so we will measure the correct power regardless of whether the coupler is directive). Now assume that the DUT is non-ideal and produces reflections as shown in Figure 2. Due to the non-ideal directivity, some of the reflected wave will "leak" into the coupled port. This "leakage" will interfere with the desired forward coupled signal and cause errors in the forward power measurement. This is a fundamental limitation of "in situ" power measurements.
Figure 2: Schematic diagram of measuring power through a through line with unknown impedance. Finite directivity causes reflected waves to contaminate the coupled signal.
As we have shown in this article, choosing a high-quality, highly directive coupler is critical for measuring RF power on a transmission line. We derived expressions that predict the forward and reverse power measurement errors and gave rules of thumb to limit the measurement errors. As a general trend, we showed that forward power measurements are less sensitive to coupler directivity than reverse power measurements.
Figure 3: Operation of a directional detector to measure (a) forward power, (b) reverse power, and (c) VSWR/return loss. The large blue arrow represents the input power, the black arrow is the power we wish to measure, and the red arrows represent interference terms due to finite directivity.
Using the definitions of directivity and vector voltage addition, we can prove that the upper and lower power errors of the forward power measurement are given by
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