Here is how engineers can measure the input power of a DUT in highly-automated measurement environments.
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, Lpi.
Figure 1 The automated measurement system employs a directional coupler and power sensor.
The Lpi loss compensates for measured Pin 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:
Pm = Pin – |Lpi| (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:
Pout = Pin – Patt (2)
Pin = Pout + Patt (3)
Now, let us divide the paths of Lpi loss into two parts, as shown in Figure 4.
Figure 4 The Lpi losses are the sum of the two parts: Lpc and Ldi.
Power sensor to input loss:
|Lpi| = |Lpc| + |Ldi| (4)
Now, moving from the point Pm or input of sensor to the point Pin or input of DUT, the Lpc loss should be added to the measured power level at Pm to reach the power level at point Pc. Finally, because Ldi is the cable loss, the Ldi loss should be subtracted from the Pc to reach power level at point Pin.
Actual input power to DUT measured by sensor:
P’in = Pm + |Lpc| – |Ldi| (5)
Now, let’s calculate the losses as shown in Figure 2.
Pin = Pm + |Lpi| = Pm + (|Lpc| + |Ldi|) (6)
This calculation looks logically correct, but as explained above, the Ldi loss shouldn’t be added to whole losses; rather, it should be subtracted from whole losses.
P’in = Pm + |Lpc| – |Ldi| (7)
To find out the error in these methods, simply use the equation below.
Error = Pin – P’in = 2 × |Ldi| (8)
Here, the inaccuracy in calculated measured power level at Pin is 2 × |Ldi| 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| = |Lpc| – |Ldi| (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 Lpc loss.
In the second stage, we measure the loss due to cable, attenuators, and hybrid coupler denoted by Ldi 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.