Technical Article

Introduction to the Directional Coupler for RF Applications

January 19, 2024 by Dr. Steve Arar

As part of a vector network analyzer (VNA), a directional coupler enables us to characterize a device’s performance by its S-parameters. Read this article to learn more about this important piece of equipment.

Directional couplers are passive elements commonly found in microwave and millimeter-wave systems. They separate the forward and backward waves in a transmission line, enabling us to determine the reflection coefficient of a DUT (device under test) by measuring the power that reflects off of the device’s input. This capability is also required to measure and control the transmitter output power level.

In this article, we’ll take a look at the main performance metrics and basic operation of directional couplers. Before that, though, let’s briefly examine one of the most important applications of directional couplers: vector network analyzers (VNAs).


Basic VNA Operation

Figure 1 illustrates the basic measurement a VNA is designed to make.


The operation of a vector network analyzer.

Figure 1. Operation of a VNA. Image used courtesy of Tektronix


A VNA uses an internal source to apply a known input to the DUT. Part of the stimulus signal is reflected at the input of the DUT. Another part of the stimulus signal passes through the DUT and appears at its output. The VNA measures the incident and reflected waves at both the input and output ports to characterize the DUT’s performance through its S-parameters. Doing so, however, requires a device that can separate the forward and backward waves.

Figure 2 shows a more detailed block diagram of the VNA’s basic operation.


Detailed diagram of a vector network analyzer's operation.

Figure 2. Detailed diagram of a VNA’s operating process. Image used courtesy of David M. Pozar


The functionality of different blocks in the above diagram will be explained later on in this series of articles. For now, just note that the DUT’s input and output ports are directly connected to signal-separation hardware that allows us to measure the forward- and backward-traveling waves. This hardware has a direct impact on the VNA’s precision, and is usually implemented as a directional coupler or a bridge. In the rest of the article, we’ll explore directional couplers in greater detail.


Directional Couplers

The basic idea of a directional coupler is to use two coupled structures to separate forward and backward waves. These coupled structures can be realized in:

  • Microstrip.
  • Stripline.
  • Coax.
  • Waveguide.


Need to find the parameters of a microstrip, stripline, coaxial cable, or waveguide? The All About Circuits website includes a range of helpful RF calculators.    


To better understand the operation of these devices, consider the two-hole waveguide directional coupler shown in Figure 3.


Diagram of a two-hole waveguide directional coupler

Figure 3. A two-hole waveguide directional coupler. Image used courtesy of Steve Arar


In this case, the coupled structures are two waveguides that share a common wall with two holes. A wave entering Port 1 is mostly transmitted through to Port 2. However, a fraction of the power flowing through the primary waveguide is coupled to the secondary waveguide through the two holes. As we can see in the figure, each hole radiates a forward wave and a backward wave in the secondary waveguide.

Consider the wave that appears at Port 3. This wave consists of two components, one for each hole. The component coming from the right hole travels a longer distance than the one coming from the left hole.

By adjusting the spacing between the holes, it’s possible for the two components to be out of phase by exactly 180 degrees at the frequency of interest. If that’s the case, the wave components cancel each other out, and—ideally, at least—no power is delivered to Port 3. To obtain this cancellation, the two holes need to be spaced λ/4 apart, where λ is wavelength in the waveguide. Because it ideally has zero RF power, Port 3 is known as the isolated port of the directional coupler.

The wave that appears at Port 4 also consists of two wave components contributed by the two holes. In this case, however, the two wave components ideally travel the same distance regardless of the holes’ spacing. The two components are in phase and add constructively, so a fraction of the input power will appear at Port 4. This makes Port 4 the coupled port of the directional coupler.

For a given spacing between the two holes, the wave cancellation at the isolated port occurs at a specific wavelength. If the wavelength or the spacing changes, the wave cancellation won’t be perfect. It follows that the frequency band over which the coupler exhibits a satisfactory response is limited. To increase the usable bandwidth, the above theory can be extended to design a multi-hole structure.


Common Schematic Symbols

Figure 4 shows two commonly used schematic symbols for directional couplers. Keep in mind that there’s no fixed way to number the ports of directional couplers, so the port numbers here aren’t consistent with those in Figure 3.


Two schematic symbols used to represent directional couplers.

Figure 4. Two schematic symbols that represent directional couplers. Image used courtesy of David M. Pozar


A small fixed fraction of the power incident on the input port (Port 1) appears at the coupled port (Port 3). The remainder of the input power is delivered to the through port (Port 2). Ideally, no power is delivered to the isolated port (Port 4). Couplers are reciprocal circuits. Therefore, with a signal incident on Port 2, Port 1 is the through port, Port 4 is the coupled port, and Port 3 is the isolated port.

It’s also worthwhile to mention that the isolated port of a coupler is almost always terminated, as in Figure 5. The topmost schematic symbol in Figure 4 is generally used when the isolated port is terminated permanently.


Directional coupler with a terminated isolated port.

Figure 5. Directional coupler with a terminated isolated port. Image used courtesy of Krytar


Codirectional and Backward-Wave Couplers

In Figures 3 and 4, the coupled port is on the side of the through port. This type of directional coupler is known as a forward-wave or codirectional coupler. It’s also possible to build couplers where the coupled port is on the same side as the input port. Couplers of this type are known as backward-wave couplers.

On the left-hand side of Figure 6, sections (a) and (b) show a microstrip coupler that couples in the backward direction. On the right-hand side of the figure, section (c) shows a forward-wave waveguide coupler for comparison purposes.


A backward-wave microstrip coupler and a forward-wave waveguide coupler.

Figure 6. Sections (a) and (b): a backward-wave microstrip coupler. Section (c): a forward-wave waveguide coupler. Image used courtesy of J. C. Whitaker


For an RF wave entering Port 1, the coupled port of the microstrip coupler is on the same side as the input port. The coupled port of the waveguide implementation is on the opposite side.


Characterizing Directional Couplers

Three useful quantities for characterizing directional couplers are:

  1. The coupling factor (C).
  2. The directivity factor (D).
  3. The isolation factor (I).

In our discussion of these factors, we’ll use the following power terms from Figure 4:

  • P1, the input power.
  • P2, the through power.
  • P3, the coupled power.
  • P4, the isolated power.

The coupling factor is defined as:

$$C ~=~ 10 \log(\frac{P_1}{P_3})$$

Equation 1.


The coupling factor specifies what fraction of the input power appears at the coupled port. For example, if the coupling factor is 20 dB, 1/100 of the input power transfers to the coupled port.

The directivity parameter is given by Equation 2:

$$D ~=~ 10 \log(\frac{P_3}{P_4})$$

Equation 2.


and the isolation parameter, by Equation 3:

$$ I ~=~ 10 \log(\frac{P_1}{P_4})$$

Equation 3.


With an ideal directional coupler, the power at the isolated port is zero (P4 = 0), so we have infinite directivity and isolation. In practice, some non-zero power transfers to the isolated port. For example, with a two-hole waveguide directional coupler, the coupling holes produce reflections in the primary and secondary waveguides, and a small portion of the RF power appears at the isolated port.

The directivity (as well as the isolation) factor is a measure of the coupler’s ability to separate forward and backward waves (more on this shortly). Directivity is typically in the range of 30 to 40 dB. From the above equations, you can easily verify that the three quantities are related by:

$$I ~=~ C~+~D$$

Equation 4.


Understanding Directivity

At first, it might not be obvious why the power ratio of the coupled and isolated ports (P3 and P4) is given the name directivity. The term directivity is expected to characterize how well the directional coupler can separate the forward- and backward-traveling waves. But does the ratio of P3 and P4 characterize this feature?

To answer this question, let’s examine the response to forward and backward waves more closely. First, consider a forward-traveling wave with power P1 entering Port 1. The input signal is shown by the blue curve in Figure 7.


Forward-traveling wave.

Figure 7. Forward-traveling wave. Image used courtesy of Steve Arar


Depending on the coupling factor, a portion of the incident wave transfers to the coupled port (Port 3). Let the power of this wave component be P3,forward. Now consider a backward-traveling wave of the same power (P1) through the directional coupler: a wave of power P1 incident on Port 2.

Because Port 3 is the isolated port for this wave, the backward-traveling wave (Figure 8) should ideally have no effect on it. However, due to the non-idealities, a small portion of the backward-traveling wave also transfers to Port 3. Let the power of this component be P3,backward.


Backward-traveling wave.

Figure 8. Backward-traveling wave. Image used courtesy of Steve Arar


Let's assume that both the forward and backward waves are present. In this case, the overall wave at the coupled port (Port 3) consists of two components: the green signal from Figure 7 and the red signal from Figure 8. Clearly, the directivity of the device depends on the ratio of the power components P3,forward to P3,backward. The higher the value of P3,forward relative to P3,backward, the greater the directivity, and the closer the device is to its ideal operation.

Because directional couplers are reciprocal devices, we can find P3,backward from our first thought experiment in Figure 7. The power that transfers to the isolated port of this setup (Port 4) is equal to P3,backward. Therefore, we only need to apply a forward-traveling wave to Port 1 and measure the power that appears at the coupled and isolated ports.

The ratio of the coupled power to the power that appears at the isolated port gives us the directivity of the device. A high directivity (35 dB or greater) is usually required in the real-world applications of directional couplers. We’ll continue this discussion in a later article, when we learn how the limited directivity of directional couplers can produce errors in VNAs.


This article is Part 1 of a series on vector network analyzers. In order of publication, the articles in this series are:

  1. Introduction to the Directional Coupler for RF Applications
  2. Understanding RF Power Measurement Errors in Directional Couplers
  3. Understanding the Inner Workings of Vector Network Analyzers
  4. Understanding the Significance of Dynamic Range and Spurious-Free Dynamic Range
  5. How to Estimate and Enhance the Dynamic Range of a Vector Network Analyzer
  6. Introduction to VNA Calibration Techniques
  7. Understanding the Limits of VNA Calibration
  8. Understanding the 12-Term Error Model and SOLT Calibration Method for VNA Measurements
  9. Understanding RF Calibration Using Short, Open, Load, and Through Terminations


Featured image used courtesy of Keysight