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14.3 Calibrated Signal Generators, Grid Dip Meters, and Component Testing

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ACMA Amateur Radio Advanced Recognition Certificate - Theory Exam

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1 Chapter 1: DC Theory, Circuit Laws & Passive Components

1.1 DC Circuit Analysis, Ohm's Law, and Kirchhoff's Laws 1.2 AC Fundamentals, Sine Waves, Peak, RMS, and Phase Relationships 1.3 Inductance, Capacitance, Reactance, and Time Constants

2 Chapter 2: Impedance, Resonance & Passive Filters

2.1 Complex Impedance, Phasors, and AC Circuit Analysis 2.2 Series and Parallel LC Resonance and Q Factor 2.3 Passive Filters, Cutoff Frequency, and Attenuator Pads

3 Chapter 3: Semiconductor Devices & Power Supplies

3.1 Semiconductor Diodes, Zener Regulators, and Rectifier Circuits 3.2 Bipolar Junction Transistors, FETs, and Operational Amplifiers 3.3 Thermionic Valves (Vacuum Tubes) and High-Power Linear Amplifiers 3.4 DC Power Supplies, Filter Networks, and Voltage Regulators

4 Chapter 4: Oscillators & Frequency Synthesis

4.1 RF Oscillators, LC Tank Topologies, and Frequency Stability 4.2 Phase-Locked Loops (PLLs) and Frequency Synthesisers 4.3 Direct Digital Synthesis (DDS), SDR Architectures, and Digital Filter Topologies

5 Chapter 5: RF Amplifiers & Linearity

5.1 Classes of Amplification, Conduction Angles, and Operating Efficiency 5.2 RF Power Amplifiers, Push-Pull Topologies, and Output Matching 5.3 Amplifier Stability, Neutralisation, and Intermodulation Distortion

6 Chapter 6: Modulation & Demodulation

6.1 Amplitude Modulation, Double Sideband, and Single Sideband (SSB) 6.2 Frequency Modulation, Phase Modulation, and FM Detectors 6.3 Digital Modulation Modes, Spectral Efficiency, and Weak-Signal Protocols

7 Chapter 7: Transmitters, Mixers & Receivers

7.1 RF Mixers, Frequency Translation, and Intermodulation 7.2 Transmitter Architectures, CW Keying, and Output Filtering 7.3 Superheterodyne Receiver Design, IF Selection, and Image Rejection 7.4 Receiver Performance Specifications, Dynamic Range, and Selectivity

8 Chapter 8: Transmission Lines & Waveguides

8.1 Transmission Line Characteristics, Impedance, and Velocity Factor 8.2 Standing Waves, Reflection Coefficient, SWR, and Return Loss 8.3 Resonant Line Sections, Quarter-Wave Transformers, and Stubs

9 Chapter 9: Impedance Matching & Baluns

9.1 Lumped-Element Matching Networks and Antenna Tuning Units 9.2 Baluns, Ununs, and Common-Mode Current Choking 9.3 Feedline Losses, High-SWR Stress, and Coaxial Installation Practice

10 Chapter 10: Practical Antennas & Arrays

10.1 Resonant Dipoles, Inverted-Vs, and Multiband Wire Antennas 10.2 Quarter-Wave Verticals, Ground Systems, and Radiation Efficiency 10.3 Parasitic Arrays, Yagi-Uda Antennas, and Quad Arrays 10.4 Antenna Gain, Aperture Antennas & Horns, ERP/EIRP, Radiation Patterns

11 Chapter 11: Radio Wave Propagation & Ionospheric Mechanics

11.1 Electromagnetic Wave Fundamentals, Polarisation, and Ground Waves 11.2 The Ionosphere, Solar Radiation, and Solar Cycles 11.3 Critical Frequency, Maximum Usable Frequency, and HF Propagation Paths

12 Chapter 12: VHF/UHF Propagation & Space Communications

12.1 Line-of-Sight, Tropospheric Ducting, and Diffraction 12.2 Sporadic-E, Auroral Scatter, and Trans-Equatorial Propagation 12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

13 Chapter 13: Test Equipment & RF Measurements

13.1 Decibels, Power Ratios, and Cascaded Stage Calculations 13.2 RF Power Meters, Directional Couplers, and Dummy Loads 13.3 Multirange Meters, Waveform Diagnostics, Oscilloscopes, and Frequency Counters

14 Chapter 14: Advanced RF Analysis & Diagnostics

14.1 Spectrum Analyser Architecture, Operation, and Spectral Purity 14.2 Antenna Analysers, Vector Network Analysers, and Smith Charts 14.3 Calibrated Signal Generators, Grid Dip Meters, and Component Testing

15 Chapter 15: Electromagnetic Compatibility & Interference

15.1 Sources of Interference, Coupling Mechanisms, and Audio Rectification 15.2 Receiver Susceptibility, Desensitisation, and Front-End Intermodulation 15.3 Practical RFI Suppression, Filter Design, and Bonding Techniques

16 Chapter 16: Electrical, RF & Station Safety

16.1 Biological Effects of RF Energy and ARPANSA Exposure Standards 16.2 Safe Separation Distances, Power Density, and Duty Cycles 16.3 Station Electrical Safety, Battery Hazards, and Safe Headphone Use 16.4 Mast and Tower Construction, Power Line Clearance, and Lightning Protection

14.3 Calibrated Signal Generators, Grid Dip Meters, and Component Testing

Key Takeaways Explain This Topic AI

Choose a calibrated 50 Ω 50\ \Omega 50 Ω RF generator whose frequency/level accuracy, spectral purity and output range suit the test. A selected level of − 140 dBm -140\text{ dBm} − 140 dBm corresponds to about 0.0224 μ V rms 0.0224\ \mu\text{V}_{\text{rms}} 0.0224 μ V rms ​ across 50 Ω 50\ \Omega 50 Ω ; that capability must be established from the instrument specification.

Receiver sensitivity is rigorously quantified using Minimum Discernible Signal (MDS), defined as the generator input power that elevates the receiver audio output by 3 dB 3\text{ dB} 3 dB ( ( Signal + Noise ) / Noise = 2 : 1 (\text{Signal} + \text{Noise}) / \text{Noise} = 2:1 ( Signal + Noise ) / Noise = 2 : 1 ).

The IARU Region1 S-meter recommendation uses S 9 = − 73 dBm S9=-73\text{ dBm} S 9 = − 73 dBm ( 50 μ V 50\ \mu\text{V} 50 μ V across 50 Ω 50\ \Omega 50 Ω ) below 30 MHz 30\text{ MHz} 30 MHz and − 93 dBm -93\text{ dBm} − 93 dBm ( 5.0 μ V 5.0\ \mu\text{V} 5.0 μ V ) above 30 MHz 30\text{ MHz} 30 MHz , with 6 dB 6\text{ dB} 6 dB per S-unit. Actual receivers may differ.

A dip meter finds resonance by weakly coupling its oscillator to an unpowered tuned circuit. Resonant loading reduces oscillator RF amplitude; a traditional grid-current indicator or a solid-state RF detector shows the dip.

Reduce dip-meter coupling and retune until a further reduction changes the indicated resonance little; excessive coupling can pull the oscillator frequency. In absorption-wavemeter mode, the oscillator is disabled and the instrument passively detects RF from an operating source.

Last updated: November 2026

14.3 Calibrated Signal Generators, Grid Dip Meters, and Component Testing

Diagnosing, aligning, and evaluating radio equipment requires two fundamental diagnostic capabilities: the ability to inject a known, highly calibrated RF signal into a receiver system, and the ability to determine the resonant frequency of unpowered passive components and circuits without applying destructive transmitter power. These roles are fulfilled respectively by the calibrated laboratory RF signal generator and the dip oscillator (historically known as the grid dip meter, or GDO). Mastering these instruments is essential for advanced amateur radio maintenance, filter alignment, and component measurement.

Calibrated RF Signal Generators

A calibrated RF signal generator supplies a test signal with specified frequency, amplitude and spectral purity for controlled injection into equipment. Its usable frequency/level range, output matching, phase noise, harmonics and calibration accuracy must suit the measurement. Example Laboratory Signal-Generator Output Stage

  • Synthesiser --> [Variable level / amplifier / filter] --+--> [Step attenuator] --> 50 ohm output
  • ^ |
  • | v
  • +------ [ALC comparator / detector]
  • ^
  • Level reference

The detector samples before the large output attenuation.

Key Architectural Features

Synthesised Frequency Engine: DDS and/or PLL synthesis referenced to a stable quartz oscillator provides precise frequency setting. TCXO/OCXO options, frequency accuracy, ageing and tuning resolution are specified separately; a sub-Hertz tuning step does not itself guarantee a particular frequency accuracy.

Automatic Level Control (ALC): A closed-loop leveling circuit monitors RF output voltage ahead of the attenuator with a precision wideband detector, adjusting PIN diode modulators to maintain constant output amplitude across the entire frequency range.

Precision 50 Ω 50\ \Omega 50 Ω Attenuator: Switched attenuation combines with the ALC level range to obtain low output levels. Step sizes and total range depend on the model. Shielding and sound connections are essential because leakage bypassing the attenuator can dominate a weak test signal; verify the specified level accuracy and leakage performance for sensitivity work.

Power and Voltage Relationships in a 50 Ω 50\ \Omega 50 Ω System

Signal generator output is calibrated in two equivalent units: decibels relative to one milliwatt ( dBm \text{dBm} dBm ) and root-mean-square microvolts ( μ V \mu\text{V} μ V ) across a standard 50 Ω 50\ \Omega 50 Ω resistive termination. P Watts = V RMS 2 R = V RMS 2 50 P_{\text{Watts}} = \frac{V_{\text{RMS}}^2}{R} = \frac{V_{\text{RMS}}^2}{50} P Watts ​ = R V RMS 2 ​ ​ = 50 V RMS 2 ​ ​

Converting milliwatts to decibels: P dBm = 10 log ⁡ 10 ( P Watts 10 − 3 W ) = 10 log ⁡ 10 ( V RMS 2 / 50 10 − 3 ) P_{\text{dBm}} = 10 \log_{10}\left(\frac{P_{\text{Watts}}}{10^{-3}\text{ W}}\right) = 10 \log_{10}\left(\frac{V_{\text{RMS}}^2 / 50}{10^{-3}}\right) P dBm ​ = 10 lo g 10 ​ ( 1 0 − 3 W P Watts ​ ​ ) = 10 lo g 10 ​ ( 1 0 − 3 V RMS 2 ​ /50 ​ )

Conversely, given power in dBm \text{dBm} dBm , the equivalent RMS voltage across 50 Ω 50\ \Omega 50 Ω is: V RMS = 50 × 10 ( P dBm − 30 10 ) V_{\text{RMS}} = \sqrt{50 \times 10^{\left(\frac{P_{\text{dBm}} - 30}{10}\right)}} V RMS ​ = 50 × 1 0 ( 10 P dBm ​ − 30 ​ ) ​ Reference Calibration Milestones (50 Ω System)

  • Output Level (dBm) RMS Voltage Significance
  • ----------------- ----------- ------------
  • +13 dBm 1.0 V Example generator output level (20 mW)
  • 0 dBm 224 mV (0.224 V) Laboratory 1.0 mW standard
  • 73 dBm 50.1 µV HF S9 Standard (IARU Region 1, < 30 MHz)
  • 93 dBm 5.01 µV VHF/UHF S9 Standard (> 30 MHz)
  • 107 dBm 1.0 µV Common reference for receiver sensitivity
  • 127 dBm 0.1 µV Example low-level test signal
  • 140 dBm 0.0224 µV Example very weak test signal
  • Receiver Testing Applications Receiver Sensitivity / MDS Testing
  • [ Calibrated Signal ] =====( Double-Shielded Coax )=====> [ Receiver Under Test ]
  • [ Generator (50 Ω) ] [ (CW Mode, 500 Hz BW) ]
  • |
  • Audio Output
  • |
  • v
  • [ True-RMS AC Voltmeter ]
  • (or Audio Power Meter)
  • 1. Minimum Discernible Signal (MDS) and Noise Floor Testing

The fundamental metric defining a receiver's absolute sensitivity is its Minimum Discernible Signal (MDS) , also designated the receiver's noise floor ( P MDS P_{\text{MDS}} P MDS ​ ).

Testing Procedure:

Terminate the receiver antenna input with a calibrated 50 Ω 50\ \Omega 50 Ω signal generator via a high-isolation, double-shielded coaxial cable.

Set the receiver to CW mode with Automatic Gain Control (AGC) disabled (or set to manual RF gain) and a standard CW intermediate-frequency filter (typically B = 500 Hz B = 500\text{ Hz} B = 500 Hz ). Connect a true-RMS audio voltmeter or audio power meter across the loudspeaker terminals.

Switch the generator RF output off while maintaining the specified 50 Ω 50\ \Omega 50 Ω source termination, and record baseline audio voltage V noise V_{\text{noise}} V noise ​ . It includes source-termination thermal noise and receiver-added noise. If an attenuated signal is used instead, verify that it is well below the expected MDS; − 145 dBm -145\text{ dBm} − 145 dBm is not automatically negligible.

Turn on the generator, tuned to the receiver passband center (e.g., 700 Hz 700\text{ Hz} 700 Hz audio beat tone). Increase generator output until the audio voltmeter reading increases by exactly 3 dB 3\text{ dB} 3 dB (a voltage increase by a factor of 2 ≈ 1.414 \sqrt{2} \approx 1.414 2 ​ ≈ 1.414 ):

V signal+noise V noise = 2 ⟹ P signal+noise P noise = 2.0 ( + 3 dB ) \frac{V_{\text{signal+noise}}}{V_{\text{noise}}} = \sqrt{2} \implies \frac{P_{\text{signal+noise}}}{P_{\text{noise}}} = 2.0 \quad (+3\text{ dB}) V noise ​ V signal+noise ​ ​ = 2 ​ ⟹ P noise ​ P signal+noise ​ ​ = 2.0 ( + 3 dB )

The generator output level in dBm \text{dBm} dBm producing this 3 dB 3\text{ dB} 3 dB rise is the MDS . In modern high-grade HF receivers, MDS is typically − 138 dBm -138\text{ dBm} − 138 dBm to − 142 dBm -142\text{ dBm} − 142 dBm in a 500 Hz 500\text{ Hz} 500 Hz bandwidth.

Theoretical Noise Floor Relationship:

For a matched source at the standard reference temperature of about 290 K 290\text{ K} 290 K , the input-referred receiver noise floor in equivalent noise bandwidth B B B is approximately:

P n = − 174 dBm/Hz + 10 log ⁡ 10 ( B ) + NF P_n = -174\text{ dBm/Hz} + 10 \log_{10}(B) + \text{NF} P n ​ = − 174 dBm/Hz + 10 lo g 10 ​ ( B ) + NF

where B B B is in hertz and NF \text{NF} NF is the receiver noise figure in decibels. A receiver with NF = 0 dB \text{NF}=0\text{ dB} NF = 0 dB adds no noise beyond the source thermal noise. Assuming B = 500 Hz B=500\text{ Hz} B = 500 Hz :

P n = − 174 + 10 log ⁡ 10 ( 500 ) = − 174 + 27 = − 147 dBm P_n = -174 + 10 \log_{10}(500) = -174 + 27 = -147\text{ dBm} P n ​ = − 174 + 10 lo g 10 ​ ( 500 ) = − 174 + 27 = − 147 dBm

A practical receiver with an 8 dB 8\text{ dB} 8 dB noise figure exhibits an MDS = − 147 + 8 = − 139 dBm \text{MDS} = -147 + 8 = -139\text{ dBm} MDS = − 147 + 8 = − 139 dBm .

2. S-Meter Calibration Standards

The S-meter on a communications receiver monitors Automatic Gain Control (AGC) voltage to indicate incoming signal strength. Historically, uncalibrated consumer receivers used arbitrary S-meter scales. To establish scientific uniformity, the International Amateur Radio Union (IARU) Region 1 adopted a definitive technical recommendation:

Important

IARU Region1 S-Meter Recommendation:

Below 30 MHz 30\text{ MHz} 30 MHz : The S 9 S9 S 9 reference is − 73 dBm -73\text{ dBm} − 73 dBm , approximately 50 μ V 50\ \mu\text{V} 50 μ V RMS across 50 Ω 50\ \Omega 50 Ω .

Above 30 MHz 30\text{ MHz} 30 MHz : The recommended S 9 S9 S 9 reference is − 93 dBm -93\text{ dBm} − 93 dBm , approximately 5.0 μ V 5.0\ \mu\text{V} 5.0 μ V RMS across 50 Ω 50\ \Omega 50 Ω .

S-Unit Progression: The recommended interval below S 9 S9 S 9 is 6 dB 6\text{ dB} 6 dB , approximately twice the signal voltage or four times the power.

Above S9: Readings are expressed directly in decibels above the S 9 S9 S 9 reference, such as S 9 + 20 dB S9+20\text{ dB} S 9 + 20 dB .

These are calibration references, not a guarantee of an individual receiver's meter accuracy. Check its tracking with a calibrated generator. IARU HF S-Meter Signal Level Scale (50 Ω System)

  • S-Unit: S1 S2 S3 S4 S5 S6 S7 S8 S9 S9+20dB
  • dBm: -121 -115 -109 -103 -97 -91 -85 -79 -73 -53
  • µV (RMS): 0.20 0.40 0.79 1.58 3.16 6.31 12.6 25.1 50.1 501.0
  • <------------------ 6 dB per S-Unit ------------------>

Using a calibrated signal generator, an amateur tests receiver S-meter tracking by injecting − 73 dBm -73\text{ dBm} − 73 dBm to verify S 9 S9 S 9 , − 79 dBm -79\text{ dBm} − 79 dBm for S 8 S8 S 8 , and so forth. In practice, many commercial transceivers exhibit poor S-meter linearity, compressing lower S-units to 2 − 3 dB 2-3\text{ dB} 2 − 3 dB per unit while expanding upper units.

3. Receiver Selectivity and Filter Passband Profiling

With AGC disabled and the receiver in its linear range, establish an on-frequency audio reference, then step the generator off-frequency while increasing its level to restore that output. This gives attenuation versus offset. A common receiver shape-factor convention compares the − 60 dB -60\text{ dB} − 60 dB and − 6 dB -6\text{ dB} − 6 dB bandwidths ; half-power bandwidth instead uses about − 3 dB -3\text{ dB} − 3 dB :

Shape Factor = Bandwidth at − 60 dB Bandwidth at − 6 dB \text{Shape Factor} = \frac{\text{Bandwidth at } -60\text{ dB}}{\text{Bandwidth at } -6\text{ dB}} Shape Factor = Bandwidth at − 6 dB Bandwidth at − 60 dB ​

An ideal rectangular response has shape factor 1 1 1 . For example, 3.84 kHz 3.84\text{ kHz} 3.84 kHz at − 60 dB -60\text{ dB} − 60 dB divided by 2.40 kHz 2.40\text{ kHz} 2.40 kHz at − 6 dB -6\text{ dB} − 6 dB gives 1.6 1.6 1.6 . A value closer to one means a sharper transition when compared at the same attenuation levels.

Dip Oscillators (Grid Dip Meters / Gate Dip Meters)

While signal generators evaluate active receivers, determining the resonant frequency of an unpowered passive circuit —such as an antenna trap, loading coil, parasitic choke, or uninstalled tuned circuit—is the domain of the dip oscillator . Dip Oscillator Unpowered Test Resonator

  • [Tunable LC oscillator]
  • |
  • [Exposed coil] <~~ magnetic coupling ~~> o---[ L ]---o
  • | | |
  • [RF strength detector +----||-----+
  • or grid-current meter] C
  • |

Meter dips when the resonator loads the oscillator.

1. Operating Principle: The Physics of the "Dip"

A dip oscillator consists of a calibrated, tunable LC oscillator equipped with a set of interchangeable, plug-in external inductor coils covering discrete bands from 1.5 MHz 1.5\text{ MHz} 1.5 MHz up to 250 MHz 250\text{ MHz} 250 MHz or higher:

Indication: A traditional valve grid-dip meter indicates oscillator grid current. Solid-state dip meters can instead rectify sampled RF voltage and amplify the detector output; they do not all measure gate current, and a BJT has no gate-source junction.

Coupling: Bringing the exposed oscillator coil near an accessible test coil creates mutual inductive coupling between the oscillator and the unpowered resonator.

Dip: At resonance the test circuit absorbs energy and loads the oscillator, reducing its RF amplitude. The instrument is arranged to show that reduction as a downward meter deflection. The common mechanism is resonant loading, regardless of the particular detector circuit.

  • 2. Applications in the Amateur Radio Station
  • A. Determining Resonant Frequency of Antenna Traps and Elements

Antenna traps isolate wire sections on multiband dipoles and Yagis. To verify the resonant frequency of an unpowered trap without applying transmitter power, hold the dip meter coil parallel to the trap inductor coil, slowly rotate the frequency dial, and note the frequency where the needle dips. This confirms whether the trap is tuned to the intended band (e.g., 14.15 MHz 14.15\text{ MHz} 14.15 MHz for a 20-meter trap).

B. Measuring Unknown Inductors ( L L L )

An accessible inductor can be estimated from its resonance with a known capacitor. Allow for stray capacitance and frequency-calibration error. A closed toroid may need a suitable auxiliary coupling winding or a dip meter with a capacitive probe; placing the normal coil beside it is not a reliable general method.

Connect a precision 1 % 1\% 1% silver-mica or C0G ceramic capacitor of known value (e.g., C ref = 100 pF C_{\text{ref}} = 100\text{ pF} C ref ​ = 100 pF ) in parallel across the unknown inductor ( L unknown L_{\text{unknown}} L unknown ​ ).

Couple weakly to the accessible resonator and find f 0 f_0 f 0 ​ . Keep leads short; the formula uses total capacitance, including relevant stray and probe capacitance.

Calculate the unknown inductance using Thomson's resonance formula:

f 0 = 1 2 π L ⋅ C ref ⟹ L unknown = 1 4 π 2 f 0 2 C ref f_0 = \frac{1}{2\pi \sqrt{L \cdot C_{\text{ref}}}} \implies L_{\text{unknown}} = \frac{1}{4\pi^2 f_0^2 C_{\text{ref}}} f 0 ​ = 2 π L ⋅ C ref ​ ​ 1 ​ ⟹ L unknown ​ = 4 π 2 f 0 2 ​ C ref ​ 1 ​

C. Measuring Unknown Capacitors ( C C C )

Conversely, to measure an unknown capacitor, solder it across a known standard inductor ( L ref L_{\text{ref}} L ref ​ ), dip the combination for f 0 f_0 f 0 ​ , and solve for capacitance:

C unknown = 1 4 π 2 f 0 2 L ref C_{\text{unknown}} = \frac{1}{4\pi^2 f_0^2 L_{\text{ref}}} C unknown ​ = 4 π 2 f 0 2 ​ L ref ​ 1 ​

D. Checking Coaxial Transmission Line Stubs

Quarter-wave shorted stubs and half-wave open stubs behave as parallel resonant circuits at their fundamental electrical frequency. Forming a tiny 1-turn loop at the end of the stub and coupling it to the dip meter coil allows rapid determination of the stub's true electrical resonant frequency and velocity factor.

E. Wavemeter (Absorption Frequency Meter) Mode

In absorption wavemeter mode , set the instrument's controls as specified in its manual so the tuned circuit and detector respond to external RF rather than using an oscillator-loading dip.

RF from a powered source couples to the tuned circuit; the detector produces an upward peak as the dial is tuned through that component.

Compare peaks with the expected fundamental and harmonic frequencies. A peak alone does not unambiguously distinguish a fundamental, harmonic or parasitic oscillation. Begin well away from a power stage, couple loosely to avoid overload, and do not touch live RF or high-voltage circuitry.

3. Operating Precautions: The Loose Coupling Rule

Caution

Excessive mutual coupling can pull the dip-meter oscillator frequency and broaden the dip, making the tuned circuit's resonance difficult to locate.

Reducing Coupling Error:

Bring the coil close enough to obtain a clear dip and locate the approximate resonant frequency.

Increase the separation and retune the dial as the coupling weakens. The useful distance depends on the coils and circuit; there is no universal centimetre setting.

Read a narrow, detectable dip whose indicated frequency changes little with a further reduction in coupling.

Weak coupling reduces frequency pulling; it does not eliminate every measurement error. Dial calibration, stray capacitance and circuit loading still limit accuracy.

  • Step-by-Step Worked Component Calculations
  • Worked Example 1: Measuring Unknown Inductance with a Dip Meter

A builder has an unmarked air-wound RF coil. A precision C ref = 100 pF C_{\text{ref}}=100\text{ pF} C ref ​ = 100 pF capacitor is connected across it with short leads. Weak inductive coupling gives a dip at f 0 = 7.15 MHz f_0=7.15\text{ MHz} f 0 ​ = 7.15 MHz . Assuming stray capacitance is negligible for this estimate, calculate the inductance in μ H \mu\text{H} μ H .

Calculation:

L = 1 4 π 2 f 0 2 C ref L = \frac{1}{4\pi^2 f_0^2 C_{\text{ref}}} L = 4 π 2 f 0 2 ​ C ref ​ 1 ​

Compute the denominator terms:

4 π 2 ≈ 39.4784 4\pi^2 \approx 39.4784 4 π 2 ≈ 39.4784

f 0 2 = ( 7.15 × 10 6 Hz ) 2 = 5.11225 × 10 13 Hz 2 f_0^2 = (7.15 \times 10^6\text{ Hz})^2 = 5.11225 \times 10^{13}\text{ Hz}^2 f 0 2 ​ = ( 7.15 × 1 0 6 Hz ) 2 = 5.11225 × 1 0 13 Hz 2

4 π 2 f 0 2 = 39.4784 × ( 5.11225 × 10 13 ) ≈ 2.01825 × 10 15 4\pi^2 f_0^2 = 39.4784 \times (5.11225 \times 10^{13}) \approx 2.01825 \times 10^{15} 4 π 2 f 0 2 ​ = 39.4784 × ( 5.11225 × 1 0 13 ) ≈ 2.01825 × 1 0 15

Multiply by capacitance C ref C_{\text{ref}} C ref ​ :

Denominator = ( 2.01825 × 10 15 ) × ( 100 × 10 − 12 F ) = 201,825 \text{Denominator} = (2.01825 \times 10^{15}) \times (100 \times 10^{-12}\text{ F}) = 201{,}825 Denominator = ( 2.01825 × 1 0 15 ) × ( 100 × 1 0 − 12 F ) = 201 , 825

Calculate inductance L L L :

L = 1 201,825 ≈ 4.955 × 10 − 6 H ≈ 4.96 μ H L = \frac{1}{201{,}825} \approx 4.955 \times 10^{-6}\text{ H} \approx 4.96\ \mu\text{H} L = 201 , 825 1 ​ ≈ 4.955 × 1 0 − 6 H ≈ 4.96 μ H

Result: The estimated inductance is 4.96 μ H 4.96\ \mu\text{H} 4.96 μ H under the stated capacitance and frequency assumptions. The result’s accuracy is limited by those measurements and the coupling/loading, not the number of displayed decimal places.

Worked Example 2: S-Meter Generator Output Level Determination

A communications receiver S-meter is to be tested on the 20-meter band ( 14.2 MHz 14.2\text{ MHz} 14.2 MHz ). Assuming the receiver follows the international IARU Region 1 standard ( S 9 = − 73 dBm S9 = -73\text{ dBm} S 9 = − 73 dBm , 6 dB 6\text{ dB} 6 dB per S-unit), determine:

The generator output level in dBm \text{dBm} dBm required to test an S 5 S5 S 5 reading.

The corresponding RF voltage in microvolts ( μ V \mu\text{V} μ V ) across the receiver's 50 Ω 50\ \Omega 50 Ω input.

Calculation:

Compute the required power in dBm \text{dBm} dBm :

From S 9 S9 S 9 to S 5 S5 S 5 is a drop of 4 S-units:

Δ P = 4 × 6 dB = 24 dB \Delta P = 4 \times 6\text{ dB} = 24\text{ dB} Δ P = 4 × 6 dB = 24 dB

P S 5 = P S 9 − Δ P = − 73 dBm − 24 dB = − 97 dBm P_{S5} = P_{S9} - \Delta P = -73\text{ dBm} - 24\text{ dB} = -97\text{ dBm} P S 5 ​ = P S 9 ​ − Δ P = − 73 dBm − 24 dB = − 97 dBm

Compute the equivalent voltage in μ V \mu\text{V} μ V :

Because each 6 dB 6\text{ dB} 6 dB step represents a halving of signal voltage:

  • At S 9 S9 S 9 : V = 50.1 μ V V = 50.1\ \mu\text{V} V = 50.1 μ V
  • At S 8 S8 S 8 : V = 25.1 μ V V = 25.1\ \mu\text{V} V = 25.1 μ V
  • At S 7 S7 S 7 : V = 12.6 μ V V = 12.6\ \mu\text{V} V = 12.6 μ V
  • At S 6 S6 S 6 : V = 6.31 μ V V = 6.31\ \mu\text{V} V = 6.31 μ V
  • At S 5 S5 S 5 : V = 3.16 μ V V = 3.16\ \mu\text{V} V = 3.16 μ V

Verify using the power formula:

V = 50 × 10 ( − 97 − 30 10 ) = 50 × 10 − 12.7 = 50 × 1.995 × 10 − 13 = 9.976 × 10 − 12 ≈ 3.16 × 10 − 6 V = 3.16 μ V V = \sqrt{50 \times 10^{\left(\frac{-97 - 30}{10}\right)}} = \sqrt{50 \times 10^{-12.7}} = \sqrt{50 \times 1.995 \times 10^{-13}} = \sqrt{9.976 \times 10^{-12}} \approx 3.16 \times 10^{-6}\text{ V} = 3.16\ \mu\text{V} V = 50 × 1 0 ( 10 − 97 − 30 ​ ) ​ = 50 × 1 0 − 12.7 ​ = 50 × 1.995 × 1 0 − 13 ​ = 9.976 × 1 0 − 12 ​ ≈ 3.16 × 1 0 − 6 V = 3.16 μ V

Result: The signal generator must be set to − 97 dBm -97\text{ dBm} − 97 dBm ( 3.16 μ V 3.16\ \mu\text{V} 3.16 μ V ) to indicate S 5 S5 S 5 .

Worked Example 3: Receiver Noise Figure from Measured MDS

An operator testing an amateur VHF receiver on 144.2 MHz 144.2\text{ MHz} 144.2 MHz with an equivalent noise bandwidth of 500 Hz 500\text{ Hz} 500 Hz measures a Minimum Discernible Signal (MDS) of − 136 dBm -136\text{ dBm} − 136 dBm . Calculate the receiver's Noise Figure (NF) in decibels.

Calculation:

Recall the theoretical thermal noise floor equation:

MDS = − 174 dBm/Hz + 10 log ⁡ 10 ( B ) + NF \text{MDS} = -174\text{ dBm/Hz} + 10 \log_{10}(B) + \text{NF} MDS = − 174 dBm/Hz + 10 lo g 10 ​ ( B ) + NF

Calculate the bandwidth factor for B = 500 Hz B = 500\text{ Hz} B = 500 Hz :

10 log ⁡ 10 ( 500 ) = 10 × 2.6990 ≈ + 27.0 dB 10 \log_{10}(500) = 10 \times 2.6990 \approx +27.0\text{ dB} 10 lo g 10 ​ ( 500 ) = 10 × 2.6990 ≈ + 27.0 dB

Substitute into the formula:

− 136 dBm = − 174 dBm + 27.0 dB + NF -136\text{ dBm} = -174\text{ dBm} + 27.0\text{ dB} + \text{NF} − 136 dBm = − 174 dBm + 27.0 dB + NF

− 136 dBm = − 147.0 dBm + NF -136\text{ dBm} = -147.0\text{ dBm} + \text{NF} − 136 dBm = − 147.0 dBm + NF

NF = − 136 − ( − 147.0 ) = + 11.0 dB \text{NF} = -136 - (-147.0) = +11.0\text{ dB} NF = − 136 − ( − 147.0 ) = + 11.0 dB

Result: The receiver exhibits a Noise Figure of 11 dB 11\text{ dB} 11 dB .

Comparison Table: RF Diagnostic and Measurement Instruments

Instrument Operational Domain Excitation Source Primary Measurement Functions Distinguishing Capability

Calibrated Signal Generator Receiver Input Testing Internal precision synthesiser (low phase noise) Sensitivity (MDS), S-meter tracking, AGC response, filter selectivity Calibrated stimulus within the specified level range and accuracy

Dip Oscillator (GDO) Passive Component Testing Internal tunable LC oscillator Resonant frequency of traps, coils, stubs; measures unknown L L L and C C C Tests unpowered circuits using low-power oscillator coupling

Spectrum Analyser Transmitter & Signal Analysis External signal under test Harmonics, spurious emissions, IMD products, bandwidth, phase noise Displays frequency-domain power spectrum across wide dynamic range ( > 100 dB > 100\text{ dB} > 100 dB )

Vector Network Analyser (VNA) Impedance & Network Analysis Internal swept two-port generator Complex impedance ( R ± j X R \pm jX R ± j X ), VSWR, return loss, filter insertion loss, TDR cable faults Measures both magnitude and phase ( S 11 , S 21 S_{11}, S_{21} S 11 ​ , S 21 ​ ) across frequency