Microwave Engineering  Measurements
In the field of microwave engineering, there are many applications, as already indicated in the first chapter. Therefore, using different applications, we often come across the need to measure different values such as power, attenuation, phase shift, VSWR, impedance, etc. for efficient use.
In this chapter, let us take a look at the different measurement techniques.
Power measurement
The measured microwave power is the average power at any position in the waveguide. There are three types of power measurement.

Low power measurement (0.01 mW to 10 mW)
Example  Bolometric technique

Average power measurement (10mW to 1W)
Example  Calorimeter technique

High power measurement (> 10W )
Example  Wattmeter Calorimeter
Let's examine them in detail.
Measurement of low power
Measurement of microwave power around 0.01mW to 10mW, can be understood as measurement of low power.
Bolometer is a device that is used for measurements of low microwave power. The element used in the bolometer can be of positive or negative temperature coefficient. For example, a barrater has a positive temperature coefficient, the resistance of which increases with increasing temperature. The thermistor has a negative temperature coefficient, the resistance of which decreases with increasing temperature.
Each of these can be used in the bolometer, but the change in resistance is proportional to the microwave power applied for the measurement. This bolometer is used in a bridge of the arms as one so that any imbalance caused, affects the output. An example tThe bridge circuit peak using a bolometer is shown in the following figure.
The millimeter here, see the value of the circulating current. The battery is variable, which is varied to obtain the balance, when an imbalance is caused by the behavior of the bolometer. This adjustment which is carried out in direct voltage of the battery is proportional to the micro power waves. The power management capacity of this circuit is limited.
Average power measurement
Microwave power measurement around 10mW to 1W, can be included like the average power measurement.
A special load is used, which generally maintains a certain specific heat value. The power to be measured, is applied to its input which proportionally changes the output temperature of the load that it already maintains. The difference in temperature rise, specifies the microwave input power to the load.e.
The bridge balancing technique is used here to get the output. The heat transfer method is used for power measurement, which is a calorimetric technique.
High power measurement
The measurement of microwave power around 10W to 50KW, can be understood as the measurement of high power.
High microwave power is normally measured by calorimetric wattmeters, which can be dry type and flow rate. The dry type is named so because it uses a coaxial cable which is filled with high hysteresis loss dielectric, while the flow type is named so because it uses water or oil. or a liquid which is a good microwave absorber.
The change in liquid temperature before and after entering the load, is taken for the calibration of the values. The limitations of this method are such as determination of flow rate, calibration and inthermal inertia, etc.
Measuring attenuation
In practice, microwave components and devices often provide some attenuation. The amount of attenuation offered can be measured in two ways. They are: the power ratio method and the RF substitution method.
Attenuation is the ratio of input power to output power and is normally expressed in decibels.
$ $ Attenuation: in: dBs = 10: log frac {P_ {in}} {P_ {out}} $$
Where $ P_ {in} $ = Power d 'input and $ P_ {out} $ = Output power
Power ratio method
In this method, the attenuation measurement is done in two steps.

Step 1  The input and output power of the entire microwave bench is done without the device whose attenuation is to be calculated.

Step 2  The input and output powerof the entire microwave bench is done with the device whose attenuation is to be calculated.
The ratio of these powers, when compared, gives the value of the attenuation.
The following figures are the two configurations that explain this.
Disadvantage  Power and attenuation measurements may not be accurate, when the input power is low and network attenuation is large.
RF substitution method
In this method, the attenuation measurement is done in three steps.

Step 1  The output power of the entire microwave bench is measured with the network whose attenuation is to be calculated.

Step 2  The output power of the entire microwave bench is measured by replacing the network with a precision calibrated attenuator.

Step 3  Now this attenuator is adjusted to get the same power as measured with the network.
The following figures are the two configurations that explain this.
The value adjusted to the attenuator directly gives the attenuation of the network. The disadvantage of the above method is avoided here and therefore it is a better procedure to measure the attenuation.
Phase shift measurement
Under practical working conditions, there may be a phase change of the signal from the actual signal. To measure this phase shift we use a comparison technique, by which we can calibrate the phase shift.
The configuration to calculate the phase shift is shown in the following figure.
Here, after the microwave source generates the signal, it passes through an Hplane Tjunction from lacit one port is connected to the network whose phase shift is to be measured and the other port is connected to an adjustable precision phase shifter.
The demodulated output is a 1KHz sine wave, which is observed in the connected CRO. This phase shifter is adjusted such that its 1KHz sine wave output also matches the above. Once the pairing has been carried out by observation in twomode CRO, this precision phase shifter gives us the reading of the phase shift. This is clearly understood by the following figure.
This procedure is the most used in the measurement of phase shift. Now let's see how to calculate the VSWR.
Measuring the VSWR
In all practical microwave applications, any type of impedance mismatch leads to the formation of waves The strength of these standing waves is measured by the voltage standing wave ratio ($ VSWR $). The ratio of the maximum voltageand the minimum voltage gives the $ VSWR $, which is denoted by $ S $.
$$ S = frac {V_ {max}} {V_ {min}} = frac {1 + rho} {1  rho} $$
Where, $ rho = reflection: co  efficient = frac {P_ {reflected}} {P_ {incident}} $
The measurement of $ VSWR $ can be done in two ways, Low $ VSWR $ and High $ VSWR $ measurements .
Low VSWR Measurement (S <10)
Low $ VSWR $ measurement can be done by adjusting the attenuator to get a reading on a DC millivoltmeter which is VSWR metre. Readings can be taken by adjusting the slit line and attenuator so that the DC millivoltmeter displays a full scale reading as well as a minimum reading.
Now these two reads are calculated to find the $ VSWR $ of the network.
Measurement of high VSWR (S> 10)
The measurement of high $ VSWR $ that has a value greater than 10 can be measured by a method called the double minimum . In this methode, the reading at the minimum value is taken, and the readings at the half point of the minimum value in the peak before and the peak after are also taken. This can be understood by the following figure.
Now the $ VSWR $ can be calculated by a relation, given as 
$$ VSWR = frac {lambda_ {g}} {pi (d_2d_1)} $$
Where, $ lambda_g: is: the: guided: wavelength $
$$ lambda_g = frac {lambda_0} {sqrt {1  (frac {lambda_0} {lambda_c}) ^ 2}} quad where: lambda_0: = {c} / {f} $$
Since the two minimum points are considered here, it is called the double minimum method. Now, let's learn how to measure impedance.
Measure impedance
Apart from Magic Tee we have two different methods, one uses split line and the other uses reflectometer.
Impedance using split line
In this method, the impedance is measured in utireading the split line and load $ Z_L $ and using this, $ V_ {max} $ and $ V_ {min} $ can be determined. In this method, the impedance measurement is done in two steps.
This is illustrated in the following figures.
When we try to get the values of $ V_ {max} $ and $ V_ {min} $ using a load, we get certain values. However, if the same is done by shorting the load, the minimum is shifted, either to the right or to the left. If this shift is to the left, it means that the load is inductive and if c 'is the shift to the right, it means the load is capacitive in nature. The following figure explains this.
In eRecording the data, an unknown impedance is calculated. The impedance and the reflection coefficient $ rho $ can be obtained both in magnitude and in phase.
Impedance using the reflectometer
Unlike the slit line, the reflectometer helps to find only the magnitude of the impedance and not the phase angle. In this method, two identical directional couplers but of different direction are taken.
These two couplers are used to sample the incident power $ P_i $ and the reflected power $ P_r $ of the load. The reflectometer is connected as shown in the following figure. It is used to obtain the amplitude of the reflection coefficient $ rho $, from which the impedance can be obtained.
From the reflectometer reading we have
$$ rho = sqrt {frac {P_r} {P_i}} $$
From the value of $ rho $, the $ VSWR $, that is$ S $ and the impedance can be calculated by
$$ S = frac {1 + rho} {1  rho} quad and quad frac {zz_g} {z + z_g} = rho $$
Where, $ z_g $ is a known wave impedance and $ z $ is an unknown impedance.
Although both forward and reverse wave parameters are observed here, there will be no interference due to the directional property of the couplers. The attenuator helps to maintain low input power.
Cavity resonator Q measurement
Although there are three methods such as transmission method, impedance method and decay or decrement method transient to measure Q of a cavity resonator, the simplest and most followed method is the transmission method . So let's take a look at its measurement setup.
In this method, the cavity resonator acts as the transmitting device. The output signal is plotted infunction of the frequency, which gives a resonance curve as shown in the following figure.
From the above configuration, the signal frequency of the microwave source is changed, keeping the signal level constant, then the output power is measured. The cavity resonator is tuned to this frequency, and the signal level and output power are noted again to notice the difference.
When the output is plotted, the resonance curve is obtained, from which we can notice the values of Half Power Bandwidth (HPBW) $ (2 Delta) $.
$$ 2 Delta = pm frac {1} {Q_L} $$
Where, $ Q_L $ is the loaded value
$$ or quad Q_L = pm frac {1} {2 Delta} = pm frac {w} {2 (ww_0)} $$
If the coupling between the microwave source and the cavity, as well as the coupling between detector and cavity are neglected, so
$ $ Q_L = Q_ 0: (unloaded:Q) $$
Disadvantage
The main disadvantage of this system is that the accuracy is a bit poor in very high Q systems due to narrow band operation.
We have covered many types of techniques for measuring different parameters. Now, let's try to solve some sample problems on this.