---
title: "Static and dynamic circulating calorimetry; measurables"
subject: "RF and Microwave Engineering"
chapter: 8
key: "semester_7/rf_and_microwave_engineering:static-dynamic-circulating-calorimetry"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/static-dynamic-circulating-calorimetry
site: BCT Engineering
---

# Static and dynamic circulating calorimetry; measurables

RF and Microwave Engineering · Chapter 8: RF and Microwave Measurements

- Asked in: 2081 Bhadra, 6+3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/static-dynamic-circulating-calorimetry
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-8

## Question

Explain how microwave medium power is measured with the static and dynamic circulating calorimetry. List all the microwave measurables and their respective measuring tools.

## Short answer

Static calorimetry: insulated fluid mass m absorbs RF for time t; P = m c ΔT/t. Dynamic calorimetry: fluid flows at rate v; P = ρ v c (T_out − T_in). Key measurables/tools: power (bolometer/calorimeter), frequency (cavity wavemeter), VSWR/impedance (slotted line), S‑parameters (VNA), noise (noise figure meter).

## Answer

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.

```text
 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:

```text
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.

```text
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:

```text
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

| Quantity measured | Measuring tool |
|---|---|
| Power (low) | Bolometer/thermistor bridge, diode detector |
| Power (medium/high) | Thermocouple, calorimeter wattmeter |
| Frequency | Cavity wavemeter, frequency counter |
| Guide wavelength | Slotted line with probe |
| VSWR / reflection coefficient | Slotted line + VSWR meter, reflectometer |
| Impedance | Slotted line + Smith chart, network analyzer |
| Attenuation / insertion loss | Power ratio or RF substitution method |
| S-parameters | Vector network analyzer |
| Q of cavity | Swept frequency / transmission method |
| Noise figure | Noise source + noise figure meter |
| Spectrum | Spectrum analyzer |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. 0.2 kg of water (c = 4186) warms by 5 °C in 120 s. What power was absorbed?
   A. About 3.5 W
   B. About 34.9 W
   C. About 349 W
   D. About 4186 W
   Answer: B. P = m c dT / t = 0.2 x 4186 x 5 / 120 = about 34.9 W. (Key point: Static calorimeter formula)

2. What is the main difference between static and dynamic calorimetry?
   A. Static uses a bolometer, dynamic uses a thermocouple
   B. Static measures frequency, dynamic measures power
   C. Static fluid flows, dynamic is insulated and still
   D. Static load is a fixed insulated mass; dynamic fluid flows continuously
   Answer: D. The static load is insulated and does not flow, while in dynamic calorimetry the fluid flows through the load continuously. (Key point: Static vs dynamic)

3. Which expression gives power in a flow calorimeter?
   A. P = rho v c (T_out - T_in)
   B. P = m c / (dT t)
   C. P = (T_out + T_in)/rho v
   D. P = c dT / v
   Answer: A. Mass flow rate (rho v) times specific heat times temperature rise gives the power carried away. (Key point: Dynamic formula)

4. Which tool is matched correctly with its quantity?
   A. Frequency: slotted line with VSWR meter
   B. Spectrum: cavity wavemeter
   C. S-parameters: vector network analyzer
   D. Noise figure: calorimeter
   Answer: C. S-parameters are measured by a VNA; frequency by wavemeter/counter; spectrum by spectrum analyzer; noise figure by noise source plus noise figure meter. (Key point: Measurement tools)

## Related in RF and Microwave Engineering

- [Power measurement with circulating calorimeter](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Acirculating-calorimeter-power) — RF and Microwave Engineering, chapter 8, asked 2×
- [Microwave vs low frequency measurement; static calorimeter](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Ameasurement-differences-static-calorimeter) — RF and Microwave Engineering, chapter 8
- [Power measurement with static calorimeter](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Astatic-calorimeter-power) — RF and Microwave Engineering, chapter 8, asked 2×
- [Device to measure 7.5 mW microwave power](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Ameasure-7-5mw-power) — RF and Microwave Engineering, chapter 8
- [Microwave vs traditional systems and need of S-parameters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Amicrowave-distinction-s-parameter-need) — RF and Microwave Engineering, chapter 1
- [Static and dry calorimeters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Astatic-dry-calorimeters) — RF and Microwave Engineering, chapter 8

## Related in other subjects

- [Static vs dynamic mathematical model](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Astatic-vs-dynamic-math-model) — Simulation and Modeling, chapter 2, asked 3×
- [Static vs dynamic implementation of list](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Astatic-vs-dynamic-list-example) — Data Structure and Algorithm, chapter 3, asked 2×
- [Static and dynamic hazards and their elimination](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Astatic-dynamic-hazards) — Digital Logic, chapter 3, asked 2×
- [Static versus dynamic binding trade-offs](https://www.bctengineer.com/question.md?key=semester_3%2Fobject_oriented_programming%3Astatic-vs-dynamic-binding) — Object Oriented Programming, chapter 7