RF and Microwave Measurements

Bolometry measures microwave power by the change in resistance of a small temperature-sensitive resistor (bolometer) when it absorbs the microwave power. It is a substitution method: the RF heating is compared with an equal amount of DC (or low-frequency) heating.

Bolometer elements

Barretters are fast but fragile and burn out easily; thermistors are more rugged and are preferred.

Working principle (balanced bridge)

          +----R1----+----R2----+
          |          |          |
   DC  ---+        [ G ]        +---
  bias    |          |          |
          +----R3----+---[Rb]---+
                          |
                   bolometer in
                   waveguide mount
                   (RF input)

1. The bolometer is one arm of a Wheatstone bridge and sits in a matched waveguide or coaxial mount that absorbs the RF power.
2. With no RF, DC bias current is adjusted until the bolometer reaches the balance resistance (e.g. 200 Ω) and the galvanometer reads zero. DC power P1 = I1²Rb.
3. RF power is applied. The bolometer heats and its resistance changes, unbalancing the bridge.
4. The DC bias is reduced until the bridge balances again (same Rb, same temperature). DC power P2 = I2²Rb.
5. The RF power equals the reduction in DC power:

P_RF = P1 − P2 = (I1² − I2²)·Rb

Example: Rb = 200 Ω, I1 = 10 mA, I2 = 8 mA → P_RF = (1×10⁻⁴ − 0.64×10⁻⁴)×200 = 7.2 mW.

Self-balancing bridge

In practical power meters, an amplifier automatically adjusts the bias to keep the bridge balanced. A second, identical thermistor (not exposed to RF) in another bridge compensates for ambient temperature changes.

Features

• Range: about 1 µW to 10 mW (low power); higher power is measured with a calibrated attenuator or directional coupler in front.
• Accuracy: about ±1–5 %; errors come from mount mismatch, mount losses (mount efficiency) and DC–RF substitution error.
• Slow response (thermal), so it measures average power.

A calorimeter measures high microwave power by converting it completely into heat in a load and measuring the temperature rise. In a static calorimeter, a fixed (non-flowing) mass of absorbing material is heated.

Principle

P = m·c·ΔT / t
m  = mass of absorbing load (kg)
c  = specific heat (J/kg·°C)
ΔT = temperature rise (°C) in time t (s)

Construction and working

 RF in      insulated (thermally isolated) load
 ======[ waveguide ]==[ absorbing load ]
                         |  thermometer /
                         |  thermocouple
                      [ ΔT readout ]

1. A matched, thermally insulated load (water, lossy dielectric or absorbing block) terminates the waveguide.
2. The microwave power is applied for a known time t; the load absorbs all of it.
3. The temperature rise ΔT is measured with a thermometer or thermocouple.
4. Power is calculated from P = m·c·ΔT/t. To remove the need to know m and c exactly, the same load is calibrated by applying a known DC or 50 Hz power and noting its temperature rise (substitution method):

P_RF = P_DC × (ΔT_RF / ΔT_DC)   (same time)

Example

A 0.1 kg water load (c = 4186 J/kg·°C) rises by 2.4 °C in 60 s:

P = 0.1 × 4186 × 2.4 / 60 = 16.74 W

Features

• Suitable for medium to high power (watts to kilowatts); accurate (about ±1 %) because it is an absolute method.
• Slow; heat losses through insulation and the mount cause error, so good thermal isolation is needed.
• For continuous high power, the circulating (flow) calorimeter is used instead.

A Vector Network Analyzer (VNA) measures the magnitude and phase of the S-parameters of a device under test (DUT) over a range of frequencies. A scalar analyzer measures magnitude only.

Block diagram

 +----------+    +-----------+    port 1   +-----+   port 2
 | Swept RF |--->| Test set: |============>| DUT |=========+
 | source   |    | couplers, |<============|     |<========+
 +----------+    | switch    |             +-----+
                 +-----------+
                   | a1  b1  b2 (a2)
                   v
        +--------------------------+
        | Receivers: mixers (LO),  |
        | IF filters, ADC          |
        +--------------------------+
                   v
        +--------------------------+
        | Processor: ratios, error |
        | correction, display      |
        +--------------------------+

Working principle

1. Source: a synthesised swept source generates the test signal over the chosen band.
2. Test set: a switch sends the signal to port 1 (forward) or port 2 (reverse). Directional couplers (or bridges) sample the incident wave a1 and the reflected wave b1 at port 1, and the transmitted wave b2 at port 2.
3. Receivers: the sampled waves are down-converted by mixers with a common LO to a low IF, keeping their phase relations; the ADC digitises them.
4. Ratio measurement: the processor computes complex ratios:

S11 = b1/a1  (a2 = 0)     S21 = b2/a1  (a2 = 0)
S22 = b2/a2  (a1 = 0)     S12 = b1/a2  (a1 = 0)

Since the ratios are taken, source power variations cancel. 5. Calibration (error correction): systematic errors (directivity, source match, load match, tracking, isolation) are removed using known standards — SOLT (short, open, load, thru) or TRL. This is the 12-term error model for two ports. 6. Display: results are shown as log magnitude, phase, group delay, SWR, Smith chart or time-domain (via inverse FFT).

Uses

Measuring S-parameters of amplifiers, filters, antennas (return loss, SWR), cables; impedance matching; fault location in lines using time-domain mode.

A spectrum analyzer displays signal amplitude versus frequency (frequency domain), whereas an oscilloscope shows amplitude versus time.

Superheterodyne (swept-tuned) type:

RF in-->[Atten]-->[Mixer]-->[IF filter]-->[Log amp]
                     ^         (RBW)          |
                     |                    [Detector]
                [Swept LO]                    |
                     ^                  [Video filter]
                     |                     (VBW)
              [Ramp generator]                |
                     |                        v
                     +---->[ Display: X=freq, Y=amp ]

Working:

1. The input attenuator sets a safe level for the mixer.
2. A swept local oscillator, driven by a ramp, mixes with the input; each input frequency fin passes the fixed IF filter when fLO − fin = fIF.
3. The IF filter bandwidth is the resolution bandwidth (RBW): it decides how close two signals can be and still be seen apart.
4. A log amplifier and envelope detector give amplitude in dB; the video filter (VBW) smooths noise.
5. The same ramp drives the horizontal axis, so the screen shows amplitude vs frequency.

Key specifications: frequency range, RBW, sweep time, dynamic range, sensitivity (displayed average noise level), phase noise.

Uses: measuring harmonics, spurious signals, modulation spectra, intermodulation, noise, EMI testing and occupied bandwidth. Modern analyzers also use FFT and real-time processing.

A circulating (flow) calorimeter measures high continuous microwave power by passing a fluid (usually water) through the load at a steady rate and measuring the temperature rise of the fluid. All the absorbed power is carried away by the flowing fluid.

Principle

P = ρ·v·c·ΔT   (W)
ρ  = density of fluid (kg/m³)
v  = volume flow rate (m³/s)
c  = specific heat (J/kg·°C)
ΔT = T_out − T_in (°C)
(ρ·v = mass flow rate ṁ, so P = ṁ·c·ΔT)

Construction

           water in (T_in)
               |
 RF in ====[ water load: glass/   ]
            [ dielectric tube in  ]
            [ tapered waveguide   ]
               |
           water out (T_out)
               |
      [flow meter]  [ΔT sensor: thermocouples
                     or thermopile]

1. The load is a tube of water (or lossy liquid) placed across or along a tapered waveguide so that it is well matched and absorbs all incident power.
2. Flow system: a pump circulates water at a constant, measured rate.
3. Temperature sensors (thermocouples or thermopile) measure inlet and outlet temperatures.
4. Heat exchanger (closed loop) cools the water before it returns.

Measurement procedure

1. Start the flow and wait for steady inlet temperature.
2. Apply microwave power and wait until the outlet temperature becomes steady.
3. Read the flow rate and ΔT and compute P.
4. Substitution check: switch off RF and pass a known DC/50 Hz power through a heater in the same load to get the same ΔT; the RF power equals this known power. This removes errors from flow measurement and heat leakage.

Example

Water flow 0.5 L/min (ρv = 0.5/60 = 8.33×10⁻³ kg/s), c = 4186 J/kg·°C, ΔT = 2.87 °C:

P = 8.333×10⁻³ × 4186 × 2.87 = 100.1 W

Features

Compared with a static calorimeter, it can run continuously because heat is removed all the time, so it suits transmitters, radars and magnetrons.

Microwave power measurement finds the average power delivered to a matched load. At microwave frequencies voltage and current are hard to define (especially in waveguides), so power is the basic quantity that is measured.

Power measurement – overview

Power ranges and usual sensors:

A bolometer is a small resistor whose resistance changes with temperature when it absorbs microwave power:

• Barretter – thin platinum wire, positive temperature coefficient (R rises with heat).
• Thermistor – semiconductor bead, negative temperature coefficient (R falls with heat).

The bolometer forms one arm of a bridge. In the DC substitution method, DC bias first balances the bridge; RF power then heats the bolometer, and the DC is reduced until the bridge balances again. The DC power removed equals the RF power absorbed:

P_RF = (I1² − I2²) · R

Double channel (dual) bolometer bridge

A single bridge drifts because the thermistor also responds to room temperature changes. The double channel bridge (e.g. self-balancing thermistor mount, HP 432 type) removes this error.

 RF in
   |                              
+--v---------+         +------------+
| RF thermis-|         | Compensat- |
| tor bridge |         | ing thermis|
| (channel 1)|         | bridge (ch2)|
+-----+------+         +-----+------+
      | V_rf                 | V_c
  self-balancing         self-balancing
  amplifier              amplifier
      |                      |
      +------> Meter <-------+
          P = (V_c² − V_rf²)/(4R)

Working principle:

1. Two matched thermistors are mounted in the same thermal block, so both see the same ambient temperature.
2. Channel 1 (RF bridge): its thermistor absorbs the microwave power. A feedback amplifier automatically adjusts the bias voltage V_rf to keep the thermistor at resistance R (e.g. 200 Ω), so the bridge stays balanced.
3. Channel 2 (compensating bridge): its thermistor gets no RF; its bias V_c also keeps it at R. V_c changes only with ambient temperature.
4. With no RF, V_rf = V_c. When RF is applied, the RF bridge needs less bias, so V_rf drops.
5. The metering circuit computes the difference of the DC powers:

P_RF = (V_c² − V_rf²) / (4R)

Since temperature drift changes both channels equally, it cancels.

Advantages: automatic balance, temperature compensation, accurate (about ±1 %), direct reading, good for 1 µW – 10 mW.

The VSWR meter with a slotted line measures the standing-wave ratio on a line, and the bolometer bridge measures low microwave power (below about 10 mW).

Measuring standing waves with a VSWR meter

Set-up:

Klystron -> Isolator -> Var. -> Freq. -> Slotted -> Load
(1 kHz AM)              atten.   meter    line
                                           |
                                    probe + crystal
                                           |
                                       VSWR meter

• The source is square-wave modulated at 1 kHz.
• A probe moves along the slotted line and samples the field. A crystal detector (square law, V ∝ E²) recovers the 1 kHz envelope.
• The VSWR meter is a high-gain amplifier tuned to 1 kHz with a meter calibrated in VSWR and dB for a square-law detector.

Steps (low VSWR, S < 10, direct method):

1. Move the probe to a voltage maximum; adjust gain so the meter reads full scale (VSWR = 1.0).
2. Move the probe to the next minimum; read VSWR directly from the scale.
3. S = E_max / E_min. Also |Γ| = (S − 1)/(S + 1).
4. Twice the distance between two minima gives λg.

For high VSWR (S > 10), the double minimum method is used: find the two positions d1, d2 on either side of the minimum where power is twice the minimum (3 dB up). Then S ≈ λg / [π(d2 − d1)].

Low power measurement by bolometry

A bolometer is a temperature-sensitive resistor: a barretter (platinum wire, R rises with power) or a thermistor (semiconductor, R falls with power). It is put in a mount at the end of the line and forms one arm of a Wheatstone bridge.

        +----R1----+----R2----+
        |          |          |
  DC  --+          G          +-- 
 bias   |          |          |
        +----R3----+--Bolom.--+
                       ^ RF power

Working (DC substitution):

1. With no RF, DC bias current I1 heats the bolometer to the balance resistance R; the galvanometer G reads zero.
2. RF is applied. It also heats the bolometer, its resistance changes and the bridge unbalances.
3. The DC current is reduced to I2 until balance returns. The bolometer is again at the same R and temperature, so the RF power replaced the DC power removed:

P_RF = (I1² − I2²) · R

Example: R = 200 Ω, I1 = 8 mA, I2 = 5 mA P_RF = (64 − 25)×10⁻⁶ × 200 = 7.8 mW.

Limitations: ambient temperature drift (solved by a compensating bridge), only low power, mismatch errors.

A calorimeter measures microwave power by converting it fully into heat in a matched load and measuring the temperature rise. It is used for medium and high power (about 10 mW up to kW).

Static calorimetry

In a static calorimeter the load (a fixed mass of water, oil or a solid absorber) is thermally insulated and does not flow.

 RF in ===> [ matched load in insulated ] -- thermometer
            [ fixed mass m, sp. heat c  ]

1. Microwave power is absorbed in the load for time t.
2. The temperature rises by ΔT, read with a thermometer or thermocouple.
3. Power absorbed:

P = m · c · ΔT / t     (watts)

Example: 0.2 kg of water (c = 4186 J/kg·°C) warms by 5 °C in 120 s → P = 0.2 × 4186 × 5 / 120 ≈ 34.9 W.

The method is simple but slow, and heat loss to the surroundings must be corrected.

Dynamic (circulating / flow) calorimetry

The fluid (usually water or oil) flows continuously through the load. In steady state all absorbed power is carried away by the fluid.

cold fluid in --> [ matched RF load ] --> hot fluid out
   T_in              ^ RF power           T_out
   flow rate v       |

1. The fluid enters at T_in and leaves at T_out.
2. With flow rate v (volume/s), density ρ and specific heat c:

P = ρ · v · c · (T_out − T_in)
For water: P (W) ≈ 4.187 × v (cm³/s) × ΔT (°C)

3. The flow rate is fixed with a flowmeter; ΔT is measured by thermocouples or a temperature bridge.

Being continuous, it suits high power (kW) transmitters and has a faster reading than the static method.

Microwave measurables and tools

A calorimeter wattmeter measures high microwave power (watts to kilowatts) by absorbing it in a fluid load and comparing the heating with a known low-frequency or DC power.

Calorimeter wattmeter

Most practical calorimeter wattmeters are flow (circulating) type with a substitution balance:

            +------------+       +------------+
 oil/water->| RF load    |------>| Input head |--+
 stream     | (absorbs   |       | (temp.     |  |
            |  RF power) |       |  sensor)   |  |  bridge
            +------------+       +------------+  +--> null
            +------------+       +------------+  |  meter
 same    -> | DC/LF load |------>| Ref. head  |--+
 stream     | (heater)   |       | (temp.     |
            +------------+       |  sensor)   |
                                 +------------+

Working principle:

1. A liquid (water or oil) is pumped at a constant rate through the RF load, which is matched to the line and absorbs all the microwave power.
2. The liquid heats up; its temperature rise is sensed by a temperature-sensitive element (thermistor or thermocouple) in the input head.
3. A second, identical path has a reference head heated by a known DC or 60 Hz power.
4. Both heads form arms of a bridge. The DC power is adjusted until the bridge balances, meaning both streams have the same temperature rise.
5. Then RF power = known DC power, read on an ordinary wattmeter.

Without the reference, power can be found from the flow directly:

P = ρ · v · c · ΔT
Water: P ≈ 4.187 · v(cm³/s) · ΔT  W

Features: wide range (10 mW to several kW), accuracy about ±1–5 %, broadband (load is well matched), but slow response and bulky (pump, plumbing).

Limitations of the single bridge bolometer

1. Ambient temperature drift: the bolometer also responds to room temperature, so zero drifts; there is no compensating element.
2. Low power only: limited to about 10 mW; higher power burns out the barretter or thermistor.
3. Manual balancing: each reading needs the DC to be adjusted by hand, so it is slow and not direct reading.
4. Mismatch error: bolometer resistance changes with power, so the mount match and reflected power change.
5. DC–RF substitution error: RF and DC currents do not heat the element in exactly the same way (skin effect, current distribution).
6. Average power only: it cannot show pulse peak power directly.

RF/MW measurement is mainly based on power and wave patterns because voltage and current cannot be measured directly at these frequencies.

Major RF/MW measurement parameters

1. Power (low, medium, high; average and peak)
2. Frequency and guide wavelength (λg)
3. VSWR and reflection coefficient (Γ)
4. Impedance (load impedance, using Smith chart)
5. Attenuation and insertion loss
6. Scattering parameters (S11, S21, …)
7. Q factor of cavities
8. Noise figure, dielectric constant, phase shift

Measurement of high VSWR (S > 10): double minimum method

For high VSWR the minimum is very sharp and E_min is very small, so the direct method (E_max/E_min) is inaccurate: the crystal leaves its square-law region at E_max and the reading near the minimum is noisy. Instead the width of the minimum is measured.

Set-up:

Source -> Isolator -> Atten. -> Freq. -> Slotted -> DUT
(1 kHz AM)                      meter    line
                                          |
                                     probe+crystal
                                          |
                                      VSWR meter

Procedure:

1. Find λg: λg = 2 × distance between two successive minima.
2. Move the probe to a voltage minimum; adjust gain so the meter reads a convenient value (e.g. 3 dB on the dB scale).
3. Move the probe to one side until the reading is twice the minimum power (3 dB higher, i.e. E = √2 E_min). Note position d1.
4. Move to the other side of the minimum and find the same level; note d2.
5. Calculate:

S = √[ 1 + 1 / sin²(π(d2 − d1)/λg) ]
For large S:  S ≈ λg / [π (d2 − d1)]

 |E|
  |\                 /
  | \               /
  |  \   √2Emin    /
  |---\-----------/---
  |    \_________/
  |   d1   Emin   d2
  +--------------------> position

Example: λg = 4 cm, d2 − d1 = 0.1 cm S ≈ 4 / (π × 0.1) = 12.73; exact formula gives 12.78.

Other method for high VSWR: the calibrated attenuator method – read the attenuator change (in dB) needed to give the same meter reading at E_max and E_min; S = 10^(dB/20).

A calorimeter measures microwave power by turning all of it into heat in a matched, thermally isolated load and measuring the resulting temperature change. It is an absolute method, mainly for medium and high power.

Basic principle

Heat energy absorbed = power × time = m · c · ΔT, so

P = m · c · ΔT / t

where m = mass of the absorbing material, c = specific heat, ΔT = temperature rise in time t.

Static calorimeter

In a static calorimeter the absorbing medium does not circulate. A fixed quantity of liquid (water or oil) forms or surrounds the matched load inside a thermally insulated vessel.

   RF in
 =====+=====================
      |  insulated vessel   |
      |   +-------------+   |
      |   | water/oil   |   |-- thermometer /
      |   | (mass m)    |   |   thermocouple
      |   +-------------+   |
       =====================

Working:

1. The waveguide or coax is terminated in a tapered water/oil load matched to the line, so no power reflects.
2. RF power is applied for a known time t.
3. The liquid temperature rises by ΔT. Since the vessel is insulated, almost all heat stays in the liquid.
4. P = m c ΔT / t.

Example: m = 0.2 kg water, c = 4186 J/kg·°C, ΔT = 5 °C in t = 120 s P = 0.2 × 4186 × 5 / 120 ≈ 34.9 W.

Calibration: often a known DC heater in the same load is used to find the effective heat capacity, which removes error due to vessel and loss.

Dry calorimeter

A dry calorimeter uses a solid absorber instead of a liquid, e.g. a resistive film, lossy ceramic or a carbon/iron-loaded load with high thermal capacity.

Working:

1. The solid load is matched to the line and placed in an insulated enclosure.
2. Absorbed RF heats the load. Its temperature is sensed by a thermopile or thermocouple attached to it.
3. Either the rate of temperature rise gives P (= m c dT/dt), or the steady temperature is compared with that produced by a known DC power in the same load (DC substitution): RF power equals the DC power that gives the same thermopile output.
4. Twin-load dry calorimeters use two identical loads – one with RF, one as reference – and a differential thermopile to cancel ambient drift.

Comparison

The proper tool to test an antenna as a device under test (DUT) is a Vector Network Analyzer (VNA). It measures S-parameters (magnitude and phase) over a frequency sweep, giving the antenna's return loss, VSWR, input impedance and bandwidth; with a second antenna in an anechoic chamber it also gives gain and radiation pattern.

What is measured on the antenna

Block diagram

 +--------- Vector Network Analyzer ----------+
 | Swept  ->  Directional  ->  Port 1 --------+--> AUT
 | source     couplers                         |
 |   |          |      |                       |
 |   |      ref (a1) refl (b1)                 |
 |   v          v      v                       |
 |  LO -> Mixers/IF -> ADC -> DSP -> display   |
 |                                Port 2 <-----+-- Ref.
 +---------------------------------------------+  antenna

Working principle

1. A synthesized swept source produces a signal over the required band (e.g. 1–6 GHz).
2. Directional couplers (or bridges) separate the incident wave a1 from the wave b1 reflected by the antenna.
3. Each signal is down-converted to an IF by mixers driven by a common LO, then digitized. Because a common reference is used, both amplitude and phase are measured.
4. The processor computes the ratio S11 = b1/a1 at each frequency. From it:

Return loss = −20 log|S11|  dB
VSWR = (1 + |S11|) / (1 − |S11|)
Zin = Z0 (1 + S11) / (1 − S11)

5. Calibration (Short–Open–Load, or SOLT for two ports) is done at the cable end before measurement. It removes systematic errors (directivity, source match, tracking), so the result refers to the antenna's feed point.
6. For radiation tests, the antenna under test is placed in an anechoic chamber with a reference horn on port 2. S21 is recorded while the AUT rotates on a positioner, giving the pattern; gain follows from the Friis equation or by comparison with a standard gain horn.

Why a VNA

• Broadband, fast swept measurement.
• Gives phase, so impedance and matching networks can be designed.
• Error correction gives high accuracy compared to a slotted line.

A simple alternative is a scalar network analyzer or slotted line with VSWR meter, but these give only magnitude (VSWR) at one frequency at a time.

An Airport Surveillance Radar (ASR) is a high-power pulsed transmitter (S-band, about 2.7–2.9 GHz, peak power of the order of 1 MW, pulse width about 1 µs). A bolometer alone would burn out, so the proper choice is:

• Flow (circulating) calorimeter wattmeter with a water-cooled dummy load to measure the full average power when the radar is off-air, and
• in normal operation, a calibrated directional coupler + attenuator + thermistor (bolometer) power meter to sample a small known fraction of the power. Peak power is then found from average power and duty cycle (or with a peak-power diode sensor).

Set-up

Magnetron/  -> Directional coupler -> Antenna or
klystron Tx    (e.g. 50 dB)           water load
                     |                (flow calori-
                 attenuator (10 dB)    meter)
                     |
               thermistor mount -> power meter

Working principle

1. Flow calorimeter: water flows through a matched dummy load at a known rate v. All RF power turns into heat:

P_avg = ρ · v · c · ΔT  ≈ 4.187 · v(cm³/s) · ΔT  W

2. Coupler method: the coupler sends a fixed fraction of power (−50 dB) to the side arm; an attenuator brings it into the bolometer range (below 10 mW). The thermistor bridge reads P_meter, and:

P_avg(dBm) = P_meter(dBm) + coupling(dB)
             + attenuation(dB)

3. Peak power of rectangular pulses:

Duty cycle D = τ × PRF
P_peak = P_avg / D

Example

Assume P_peak = 1 MW, τ = 1 µs, PRF = 1000 Hz.

• D = 1×10⁻⁶ × 1000 = 0.001
• P_avg = 1 MW × 0.001 = 1 kW
• With 50 dB coupler + 10 dB attenuator (60 dB total): power at the meter = 1000 W × 10⁻⁶ = 1 mW, which suits a thermistor mount.
• In the flow calorimeter, 1 kW with ΔT = 10 °C needs a flow of 1000/(4.186 × 10) ≈ 23.9 cm³/s of water.

Reasons for this choice

• Calorimeter handles kW average power and is absolute and broadband.
• The coupler method allows monitoring while the radar operates.
• Bolometer and diode sensors are only for mW levels, so they must be used behind a coupler and attenuator.

Microwave measurement parameters are the quantities used to describe signals and components at microwave frequencies, where power and wave patterns are measured instead of voltage and current.

Major microwave measurement parameters

• Power: average or peak power delivered to a matched load (W, dBm).
• Frequency / wavelength: source frequency f and guide wavelength λg.
• VSWR: S = V_max / V_min on the line; shows mismatch.
• Reflection coefficient: Γ = (Z_L − Z0)/(Z_L + Z0); |Γ| = (S − 1)/(S + 1).
• Impedance: load impedance found from VSWR and position of minimum.
• Attenuation / insertion loss: power loss through a component in dB.
• S-parameters: reflection and transmission ratios of a network.
• Q factor: stored energy / energy lost per cycle in a cavity.
• Noise figure: degradation of SNR by a device.

Low power measurement device: the bolometer bridge

Low power (below about 10 mW) is measured with a bolometer – a temperature-sensitive resistor – in a bridge.

Types of bolometer:

• Barretter: thin platinum wire; positive temperature coefficient; sensitive but burns out easily.
• Thermistor: semiconductor bead; negative temperature coefficient; robust, commonly used.

          +---R1---+---R2---+
          |        |        |
 DC bias -+        G        +-
          |        |        |
          +---R3---+--Rb----+
                       ^
                       | microwave power
                  bolometer mount

Working principle (DC substitution):

1. With no RF, DC bias current I1 through the bolometer Rb heats it until Rb equals the value needed for balance (R1/R2 = R3/Rb); the galvanometer G reads zero.
2. The microwave power is applied to the bolometer mount. It heats the bolometer further, its resistance changes, and the bridge unbalances.
3. The DC bias is reduced to I2 until balance returns. Now Rb is again at the same value and temperature, so the drop in DC power equals the RF power:

P_RF = (I1² − I2²) · Rb

Example: Rb = 200 Ω, I1 = 8 mA, I2 = 5 mA → P_RF = (64 − 25)×10⁻⁶ × 200 = 7.8 mW.

To remove ambient temperature drift, practical meters use a self-balancing double bridge with a second compensating thermistor: P = (V_c² − V_rf²)/(4R).

Other low-power sensors: thermocouple sensors (about 1 µW–100 mW) and Schottky diode sensors (down to about 100 pW, square law below about −20 dBm).

7.5 mW is a low microwave power:

P (dBm) = 10 log10(7.5 mW / 1 mW) = 8.75 dBm

This is inside the range of a thermistor (bolometer) power meter, about 1 µW–10 mW. A diode sensor is not suitable, because it is square law only below about −20 dBm, and a calorimeter is too slow and insensitive at mW level. So the proper device is a thermistor mount with a self-balancing (double) bolometer bridge – the DC substitution bolometer method.

Bolometer element

• Thermistor: semiconductor bead, negative temperature coefficient, robust – chosen here.
• Barretter: fine platinum wire, positive temperature coefficient, more delicate.

The thermistor sits in a matched waveguide/coax mount that absorbs all the incident power.

Basic bridge (DC substitution)

          +---R1---+---R2---+
          |        |        |
 DC bias -+        G        +-
          |        |        |
          +---R3---+--Rth---+
                       ^ 7.5 mW RF

1. With no RF, DC bias current I1 heats the thermistor until it reaches the balance resistance R (e.g. 200 Ω); G reads zero.
2. RF power heats the thermistor more; R changes and the bridge unbalances.
3. DC is reduced to I2 to restore balance. The thermistor is at the same temperature, so

P_RF = (I1² − I2²) · R

Practical self-balancing double bridge

To avoid drift with room temperature and manual balancing:

1. Two matched thermistors share one thermal block. One gets RF (RF bridge), the other only sees ambient temperature (compensating bridge).
2. Feedback amplifiers keep both bridges balanced automatically, with bridge voltages V_rf and V_c.
3. The meter shows

P_RF = (V_c² − V_rf²) / (4R)

Temperature drift changes both channels equally and cancels.

Practical precautions for 7.5 mW

• Zero the meter with RF off.
• Use a well-matched mount (low VSWR) to avoid mismatch error, and apply the mount calibration factor.
• 7.5 mW is close to the 10 mW upper limit; if the level may rise, add a 10 dB attenuator (reading becomes 0.75 mW) and add 10 dB back.

Microwave measurements differ from low-frequency ones because at microwave frequencies the wavelength is comparable to circuit size, so circuits behave as distributed systems and voltage and current lose their simple meaning.

Differences from low-frequency measurements

Reasons: lead lengths are a large fraction of a wavelength, meters' own capacitance and inductance load the circuit, and transit time of electrons limits ordinary devices.

Static calorimeter for power measurement

A calorimeter turns all microwave power into heat in a matched load and measures the temperature rise. In the static type the absorbing medium does not flow.

   RF in
 =====+=====================
      |  insulated vessel   |
      |   +-------------+   |
      |   | water/oil   |   |-- thermometer /
      |   | (mass m)    |   |   thermocouple
      |   +-------------+   |
       =====================

Working:

1. A fixed mass m of liquid (or a solid absorber) forms a matched load at the end of the waveguide, inside a thermally insulated vessel.
2. RF power is applied for a time t; the load absorbs it and heats.
3. The temperature rise ΔT is measured with a thermometer, thermocouple or thermopile.
4. Since heat gained = P × t = m c ΔT,

P = m · c · ΔT / t

Example: m = 0.2 kg water, c = 4186 J/kg·°C, ΔT = 5 °C in t = 120 s P = 0.2 × 4186 × 5 / 120 ≈ 34.9 W.

5. For better accuracy, a known DC heater is placed in the same load and its power adjusted to give the same temperature rise (DC substitution); then P_RF = P_DC. This cancels heat loss and heat-capacity errors.

Features: absolute method, used for medium–high power; simple but slow and needs good thermal insulation.