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A directional coupler is used to sample a small amount of input signal power for measurement purposes. Port 1 is the input port; port 2 is the output port; port 3 is the coupled port; port 4 is the isolated/terminated port, usually terminated to 50 Ω to minimize any reflection.

However, when we measure input power to a device under test (DUT), particularly in an automated measurement system, we use a power sensor along with a directional coupler. When it comes to 1-dB compression point measurement, by varying the input power and measuring the output power, we have to measure and calculate the loss between the power sensor connected to port 3 and input to a DUT to calculate losses for correction of measured power by a power sensor (**Figure 1**). In this article, this loss is denoted as power sensor to input loss, L_{pi}.

**Figure 1** The automated measurement system employs a directional coupler and power sensor.

The L_{pi }loss compensates for measured P_{in} power level by the power sensor. At first glance, the losses would be measured as shown in **Figure 2**, but this approach to measure the loss is not correctly formulated.

Power measured by power sensor:

P_{m} = P_{in} – |L_{pi}| (1)

**Figure 2** Here is how power is measured with a power sensor.

The sign convention results of the power flow into the element are put according to the settings shown in **Figure 3**.

**Figure 3** Here is how the power flows into the element.

Power flow will yield as follows:

P_{out} = P_{in} – P_{att }(2)

P_{in} = P_{out} + P_{att }(3)

Now, let us divide the paths of L_{pi} loss into two parts, as shown in **Figure 4**.

**Figure 4** The L_{pi} losses are the sum of the two parts: L_{pc} and L_{di}.

Power sensor to input loss:

|L_{pi}| = |L_{pc}| + |L_{di}| (4)

Now, moving from the point P_{m} or input of sensor to the point P_{in} or input of DUT, the L_{pc} loss should be added to the measured power level at P_{m} to reach the power level at point P_{c}. Finally, because L_{di} is the cable loss, the L_{di} loss should be subtracted from the P_{c} to reach power level at point P_{in}.

Actual input power to DUT measured by sensor:

P’_{in} = P_{m} + |L_{pc}| – |L_{di}| (5)

Now, let’s calculate the losses as shown in Figure 2.

P_{in} = P_{m} + |L_{pi}| = P_{m} + (|L_{pc}| + |L_{di}|) (6)

This calculation looks logically correct, but as explained above, the L_{di} loss shouldn’t be added to whole losses; rather, it should be subtracted from whole losses.

P’_{in} = P_{m} + |L_{pc}| – |L_{di}| (7)

To find out the error in these methods, simply use the equation below.

Error = P_{in} – P’_{in} = 2 × |L_{di}| (8)

Here, the inaccuracy in calculated measured power level at P_{in} is 2 × |L_{di}| higher than the accurate power level.

So, the loss between power sensor and the input of DUT should be calculated using the equation below.

|Power sensor to input loss| = |L_{pc}| – |L_{di}| (9)

Finally, here is how to practically measure the losses.

**Figure 5** A more practical approach to measure the losses.

Because the directional coupler’s loss between the incident and received power is negligible, in the first step, we measure output power using a power sensor connected to the output of the directional coupler and subtract the measured power between two power sensors, which gives us L_{pc} loss.

In the second stage, we measure the loss due to cable, attenuators, and hybrid coupler denoted by L_{di} between the directional coupler and the DUT input by using a network analyzer. Finally, we calculate the whole loss according to equation 9.

*This article was originally published on EDN.*

*Siamack Ghadimi holds a PhD in electrical engineering and is a university assistant professor.*

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