7.4 Receiver Performance Specifications, Dynamic Range, and Selectivity

ACMA Amateur Radio Advanced Recognition Certificate - Theory Exam

Track your progress as you read

Finished sections get a check mark.

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

7.4 Receiver Performance Specifications, Dynamic Range, and Selectivity

Key Takeaways Explain This Topic AI

MDS is a common CW sensitivity measure: the input signal that gives 0 dB 0\text{ dB} 0 dB output SNR, or a 3 dB 3\text{ dB} 3 dB rise in total signal-plus-noise power. At 290 K 290\text{ K} 290 K , estimate it from − 174 + 10 log ⁡ 10 ( B ) + N F -174+10\log_{10}(B)+NF − 174 + 10 lo g 10 ​ ( B ) + NF in dBm, using equivalent noise bandwidth B B B in Hz. Other sensitivity specifications may use a stated SNR or SINAD.

Noise figure measures SNR degradation. External noise often permits a moderate NF on HF; lower receiver noise matters more on quiet paths and in VHF/UHF weak-signal work. Choose preamp gain for the antenna, feed loss and noise environment while preserving strong-signal headroom.

Filter selectivity is specified by its shape factor, calculated as the ratio of the bandwidth at − 60 dB -60\text{ dB} − 60 dB attenuation to the bandwidth at − 6 dB -6\text{ dB} − 6 dB attenuation; high-performance quartz crystal ladder and mechanical filters achieve shape factors of 1.5 1.5 1.5 to 1.8 1.8 1.8 , closely approaching an ideal rectangular response.

Third-Order Intermodulation Dynamic Range ( I M D 3 DR IMD3\text{ DR} I M D 3 DR ) specifies the span in dB \text{dB} dB between the MDS and the level of two equal off-channel tones whose third-order intermodulation distortion products equal the MDS, calculated as I M D 3 DR = 2 3 ( I I P 3 − MDS ) IMD3\text{ DR} = \frac{2}{3}(IIP_3 - \text{MDS}) I M D 3 DR = 3 2 ​ ( II P 3 ​ − MDS ) .

RMDR describes the limit caused by a strong off-channel signal mixing with local-oscillator phase noise and raising the in-channel noise floor. Compare RMDR, IMD3 and blocking at stated bandwidths, tone spacings and gain settings to identify the receiver's limiting mechanism.

Last updated: November 2026

7.4 Receiver Performance Specifications, Dynamic Range, and Selectivity

Evaluating the quality of a communications receiver requires far more than measuring how loud it can reproduce a weak signal. Under modern band conditions—where an operator may be searching for an elusive microvolt DX signal while multi-kilowatt stations transmit on adjacent frequencies—the true caliber of a receiver is defined by its dynamic range , noise figure , and selectivity .

A receiver that boasts high sensitivity but possesses poor dynamic range will crumble under real-world operating conditions, becoming deafened by intermodulation distortion products, phase noise reciprocal mixing, and amplifier gain blocking.

• 1. Sensitivity, Thermal Noise Floor, and Noise Figure
• The Fundamental Thermal Noise Limit

The ultimate physical limit to receiver sensitivity is set by the thermal agitation of electrons inside any resistive conductor at a temperature above absolute zero, known as Johnson-Nyquist noise . The available thermal noise power ( P n P_n P n ​ ) across an impedance-matched load is given by: P n = k ⋅ T ⋅ B P_n = k \cdot T \cdot B P n ​ = k ⋅ T ⋅ B

where:

k = 1.380649 × 10 − 23 J/K k = 1.380649 \times 10^{-23}\text{ J/K} k = 1.380649 × 1 0 − 23 J/K is Boltzmann's constant,

T T T is the absolute temperature of the conductor in Kelvin (standard reference room temperature is taken as T 0 = 290 K T_0 = 290\text{ K} T 0 ​ = 290 K ),

B B B is the equivalent noise bandwidth in hertz: the width of a rectangular filter passing the same noise power at the same peak gain.

Expressed in milliwatts and converted to decibels relative to one milliwatt ( dBm \text{dBm} dBm ) for a normalized 1 Hz 1\text{ Hz} 1 Hz bandwidth: P n ( 1 Hz ) = 10 log ⁡ 10 ( k T 0 × 1 Hz 1 mW ) = 10 log ⁡ 10 ( 1.38 × 10 − 23 × 290 10 − 3 ) = − 173.98 dBm/Hz ≈ − 174 dBm/Hz P_{n(1\text{ Hz})} = 10 \log_{10}\left( \frac{k T_0 \times 1\text{ Hz}}{1\text{ mW}} \right) = 10 \log_{10}\left( \frac{1.38 \times 10^{-23} \times 290}{10^{-3}} \right) = -173.98\text{ dBm/Hz} \approx -174\text{ dBm/Hz} P n ( 1 Hz ) ​ = 10 lo g 10 ​ ( 1 mW k T 0 ​ × 1 Hz ​ ) = 10 lo g 10 ​ ( 1 0 − 3 1.38 × 1 0 − 23 × 290 ​ ) = − 173.98 dBm/Hz ≈ − 174 dBm/Hz

This value, − 174 dBm/Hz -174\text{ dBm/Hz} − 174 dBm/Hz , represents the fundamental theoretical thermal noise floor of any passive 50 Ω 50\ \Omega 50 Ω system at room temperature.

Minimum Discernible Signal (MDS)

The Minimum Discernible Signal (MDS) is a common CW sensitivity/noise-floor measure. It is the input RF power giving a signal equal to the total output noise with a matched 290 K 290\text{ K} 290 K reference source: 0 dB 0\text{ dB} 0 dB SNR , or a 3 dB 3\text{ dB} 3 dB rise in ( S + N ) / N (S+N)/N ( S + N ) / N . Voice sensitivity may instead be specified at a stated SNR or SINAD. For the MDS criterion: MDS (dBm) = − 174 dBm/Hz + 10 log ⁡ 10 ( B ) + N F \text{MDS (dBm)} = -174\text{ dBm/Hz} + 10 \log_{10}(B) + NF MDS (dBm) = − 174 dBm/Hz + 10 lo g 10 ​ ( B ) + NF

Here B B B is equivalent noise bandwidth in hertz, and N F NF NF is receiver noise figure in dB for the same frequency and gain settings.

Noise Figure ( N F NF NF ) and Noise Factor ( F F F )

Resistors generate thermal noise; biased semiconductor junctions can also contribute shot noise from discrete charge flow. The Noise Factor ( F F F ) is the ratio of the input Signal-to-Noise Ratio to the output Signal-to-Noise Ratio: F = SNR in SNR out ≥ 1 F = \frac{\text{SNR}_{\text{in}}}{\text{SNR}_{\text{out}}} \ge 1 F = SNR out ​ SNR in ​ ​ ≥ 1

The Noise Figure ( N F NF NF ) is simply the noise factor expressed in decibels: N F (dB) = 10 log ⁡ 10 ( F ) = MDS − ( − 174 dBm/Hz + 10 log ⁡ 10 ( B ) ) NF\text{ (dB)} = 10 \log_{10}(F) = \text{MDS} - \left( -174\text{ dBm/Hz} + 10 \log_{10}(B) \right) NF (dB) = 10 lo g 10 ​ ( F ) = MDS − ( − 174 dBm/Hz + 10 lo g 10 ​ ( B ) )

HF vs. VHF/UHF Noise Figure Requirements

Useful receiver noise figure depends on the external noise reaching the antenna, feed losses and receiver design:

HF: Atmospheric, galactic and man-made noise often dominate. If that noise is already well above receiver noise, adding preamp gain gives little SNR improvement and can reduce strong-signal headroom. On a quiet upper-HF path, a lower receiver NF can still help; there is no universal 10 dB 10\text{ dB} 10 dB or 12 dB 12\text{ dB} 12 dB cutoff.

VHF/UHF and microwaves: External noise is often lower, so low receiver noise and low feed loss become more important for weak signals such as EME or troposcatter. Sky, ground and local noise still contribute. Low-noise preamplifiers are useful, but the required NF and device technology follow the system design rather than a fixed band-wide rule.

2. Selectivity and Filter Shape Factor

Selectivity defines a receiver's ability to differentiate between a desired weak signal and strong off-frequency transmissions on adjacent channels.

The Shape Factor ( S F 60 / 6 SF_{60/6} S F 60/6 ​ )

Half-power bandwidth uses the − 3 dB -3\text{ dB} − 3 dB points . Communications IF filters are also commonly specified at − 6 dB -6\text{ dB} − 6 dB , which is approximately half voltage and one-quarter power. Quote the measurement level. For skirt selectivity, the 60 / 6 60/6 60/6 shape factor is: Shape Factor ( S F 60 / 6 ) = Bandwidth at − 60 dB Bandwidth at − 6 dB \text{Shape Factor } (SF_{60/6}) = \frac{\text{Bandwidth at } -60\text{ dB}}{\text{Bandwidth at } -6\text{ dB}} Shape Factor ( S F 60/6 ​ ) = Bandwidth at − 6 dB Bandwidth at − 60 dB ​

The − 6 dB -6\text{ dB} − 6 dB bandwidth dictates the fidelity and bandwidth of the desired passband.

The − 60 dB -60\text{ dB} − 60 dB bandwidth dictates how close a strong interfering signal can approach before its skirt attenuation reaches 60 dB 60\text{ dB} 60 dB (a factor of 1 , 000 1,000 1 , 000 in voltage attenuation, or 1 , 000 , 000 1,000,000 1 , 000 , 000 in power attenuation). Relative response (dB)

• 0 ________
• / \
• 6 ---------------o----------o---------------
• / \
• / \
• 60 ------------o----------------o------------
• | | | |
• | +--- B6 ---+ |
• +------ B60 -----+ Frequency ->

B60 is wider than B6.

Example: B6 = 2400 Hz, B60 = 3600 Hz; SF60/6 = 1.5.

Ideal Brick-Wall Filter: S F = 1.0 SF = 1.0 SF = 1.0 (impossible to realize with analog components).

High-Grade 8-Pole Quartz Crystal Ladder / Collins Mechanical Filter: S F = 1.5 to 1.8 SF = 1.5\text{ to }1.8 SF = 1.5 to 1.8 (superb adjacent-channel isolation).

Typical Low-Cost Ceramic IF Filter: S F = 2.2 to 3.0 SF = 2.2\text{ to }3.0 SF = 2.2 to 3.0 .

Single LC Resonator: Its shallow skirts give poor distant-frequency rejection. In the ideal single-resonator model, S F 60 / 6 = ( 10 6 − 1 ) / ( 10 0.6 − 1 ) ≈ 579 SF_{60/6}=\sqrt{(10^6-1)/(10^{0.6}-1)}\approx579 S F 60/6 ​ = ( 1 0 6 − 1 ) / ( 1 0 0.6 − 1 ) ​ ≈ 579 . Several coupled resonators can give much steeper skirts; specify the complete filter response.

Modern Digital Signal Processing (DSP) FIR Filters: Shape factors approaching 1.15 1.15 1.15 , realized via sharp mathematical finite-impulse-response convolution algorithms.

3. Dynamic Range Metrics: IMD3, BDR, and RMDR

Dynamic range is the operational span between the weakest signal a receiver can detect (the noise floor / MDS) and the strongest off-frequency signal it can tolerate before suffering unacceptable distortion or degradation.

Two-Tone Third-Order Intermodulation Dynamic Range ( I M D 3 DR IMD3\text{ DR} I M D 3 DR )

When two strong off-channel signals at frequencies f 1 f_1 f 1 ​ and f 2 f_2 f 2 ​ enter the receiver front-end, non-linearities in the RF amplifier or first mixer generate third-order intermodulation products ( 2 f 1 − f 2 2f_1 - f_2 2 f 1 ​ − f 2 ​ and 2 f 2 − f 1 2f_2 - f_1 2 f 2 ​ − f 1 ​ ). If these spurious products fall exactly on the tuned frequency of a weak desired station, they mask the signal completely.

The I M D 3 IMD3 I M D 3 Dynamic Range is the difference in decibels between the receiver's Minimum Discernible Signal (MDS) and the power level of two equal off-channel input signals that produce a third-order IMD product equal to the MDS: I M D 3 DR (dB) = 2 3 ( I I P 3 − MDS ) IMD3\text{ DR (dB)} = \frac{2}{3} \left( IIP_3 - \text{MDS} \right) I M D 3 DR (dB) = 3 2 ​ ( II P 3 ​ − MDS )

For example, if a receiver has an MDS = − 138 dBm \text{MDS} = -138\text{ dBm} MDS = − 138 dBm and an I I P 3 = + 24 dBm IIP_3 = +24\text{ dBm} II P 3 ​ = + 24 dBm : I M D 3 DR = 2 3 ( + 24 − ( − 138 ) ) = 2 3 ( 162 ) = 108 dB IMD3\text{ DR} = \frac{2}{3} \left( +24 - (-138) \right) = \frac{2}{3}(162) = \mathbf{108\text{ dB}} I M D 3 DR = 3 2 ​ ( + 24 − ( − 138 ) ) = 3 2 ​ ( 162 ) = 108 dB

An I M D 3 DR > 100 dB IMD3\text{ DR} > 100\text{ dB} I M D 3 DR > 100 dB is the hallmark of an elite contest-grade receiver.

Blocking Dynamic Range (BDR) / Desensitisation

Blocking Dynamic Range (BDR) —also called desensitisation—measures the receiver's resistance to gain compression caused by a single monstrous off-channel carrier (such as a local broadcast transmitter or nearby amateur station located 20 kHz 20\text{ kHz} 20 kHz or 100 kHz 100\text{ kHz} 100 kHz away):

Measurement: Disable AGC and set a measurable weak wanted signal. Add a strong off-channel CW interferer at a stated spacing, such as 2 kHz 2\text{ kHz} 2 kHz or 20 kHz 20\text{ kHz} 20 kHz , and increase it until the wanted-signal output falls by 1 dB 1\text{ dB} 1 dB . Measure the wanted component separately from any noise rise. Record frequency, bandwidth and preamp settings.

Definition: BDR is the difference in decibels between the blocking signal power and the receiver MDS: BDR (dB) = P blocking (1 dB) − MDS \text{BDR (dB)} = P_{\text{blocking (1 dB)}} - \text{MDS} BDR (dB) = P blocking (1 dB) ​ − MDS

Elite transceivers achieve a 20 kHz 20\text{ kHz} 20 kHz BDR exceeding 135 dB 135\text{ dB} 135 dB to 145 dB 145\text{ dB} 145 dB .

Reciprocal Mixing Dynamic Range (RMDR)

Reciprocal Mixing Dynamic Range (RMDR) is another strong-signal limit. It can dominate close-in reception even when mixer linearity and roofing selectivity are good. Compare it with IMD and blocking results at the same spacing; improving one mechanism does not remove the others.

The Physical Mechanism: Every real-world local oscillator exhibits phase noise —random, micro-jitter phase fluctuations appearing as noise sidebands flanking the LO carrier. When a strong off-channel interfering signal ( P int P_{\text{int}} P int ​ ) enters the mixer at an offset Δ f \Delta f Δ f , it mixes with the LO's phase noise sidebands located at the same offset Δ f \Delta f Δ f .

Noise Folding: This mixing action folds (transfers) the oscillator's phase noise directly into the IF passband, dramatically elevating the receiver noise floor and obliterating weak desired signals. Local Oscillator Spectrum

• Mixer RF Port: (Phase Noise Skirts)
• ================ =========================
• Strong Interferer LO Carrier
• | |
• | Delta f | Delta f
• |<-------->| |<-------->
• | | | | Phase Noise
• v v v v Skirt
• +------------------+ +------------------+
• | Off-Channel Carrier | Phase Noise at |
• | at f_0 + Delta f | f_LO + Delta f |
• +------------------+ +------------------+
• \ /
• \ /
• -> [ RF MIXER MULTIPLICATION ] <--
• |
• v
• +---------------------------------+
• | Folded Phase Noise Floods the |
• | Receiver IF Passband! |
• +---------------------------------+

Mathematical Definition: RMDR is the difference in decibels between the receiver MDS and the power level of an off-frequency carrier that elevates the receiver noise floor by 3 dB 3\text{ dB} 3 dB : RMDR (dB) = − L ( Δ f ) − 10 log ⁡ 10 ( B ) \text{RMDR (dB)} = - \mathcal{L}(\Delta f) - 10 \log_{10}(B) RMDR (dB) = − L ( Δ f ) − 10 lo g 10 ​ ( B )

where L ( Δ f ) \mathcal{L}(\Delta f) L ( Δ f ) is the local oscillator phase noise at offset Δ f \Delta f Δ f in dBc/Hz \text{dBc/Hz} dBc/Hz , and B B B is the detection bandwidth.

If the LO has a phase noise of − 140 dBc/Hz -140\text{ dBc/Hz} − 140 dBc/Hz at 2 kHz 2\text{ kHz} 2 kHz offset and the receiver bandwidth is 500 Hz 500\text{ Hz} 500 Hz ( 27 dB 27\text{ dB} 27 dB ), the RMDR is limited to 140 − 27 = 113 dB 140 - 27 = 113\text{ dB} 140 − 27 = 113 dB . If an interfering signal exceeds this threshold, the noise floor rushes up, drowning out weak signals.

• 4. Automatic Gain Control (AGC) and S-Meter Standards
• Automatic Gain Control (AGC) Dynamics

An incoming antenna signal can range from 0.05 μ V 0.05\ \mu\text{V} 0.05 μ V ( − 133 dBm -133\text{ dBm} − 133 dBm ) up to 100 mV 100\text{ mV} 100 mV ( − 7 dBm -7\text{ dBm} − 7 dBm )—an astronomical dynamic range of 126 dB 126\text{ dB} 126 dB (a power ratio of nearly four trillion to one). The human ear cannot tolerate such volume swings.

AGC Operation: The AGC system samples the IF signal after the selectivity filters, rectifies it into a negative DC control voltage, and applies this voltage to the control grids or gates of variable-gain IF amplifier stages. As signal strength increases, the AGC voltage reduces amplifier gain, holding the audio output volume virtually constant across a 100 dB 100\text{ dB} 100 dB input change.

Time Constants:

Attack Time: The time taken to reduce gain after a signal rises. Fast attack, often a few milliseconds, reduces audio overshoot. It does not set a safe headphone sound level; keep listening volume modest and use suitable transient protection.

Decay/Recovery Time: Sets how quickly gain returns after the strong signal falls. A separate hang/hold time can delay the start of that recovery.

Slow recovery (for example 1 s 1\text{ s} 1 s to 2 s 2\text{ s} 2 s ) is often useful for SSB because it reduces noise pumping between words.

Fast recovery (for example 50 ms 50\text{ ms} 50 ms to 100 ms 100\text{ ms} 100 ms ) can help CW reception recover sooner after a strong signal. Recovery is finite; choose the setting for signal speed, fading and interference.

IARU Region 1 S-Meter Calibration Recommendation

IARU Region 1 recommends the following S-meter references. They are useful calibration conventions; practical meter readings can differ, so check the receiver specification and calibration:

Operating Band S9 Signal Generator Voltage ( V RMS V_{\text{RMS}} V RMS ​ into 50 Ω 50\ \Omega 50 Ω ) S9 Equivalent Power ( P in P_{\text{in}} P in ​ in dBm \text{dBm} dBm ) Calibration Increment per S-Unit

HF Bands ( < 30 MHz < 30\text{ MHz} < 30 MHz ) 50.0 μ V 50.0\ \mu\text{V} 50.0 μ V − 73.0 dBm -73.0\text{ dBm} − 73.0 dBm 6.0 dB 6.0\text{ dB} 6.0 dB per S-unit (Voltage ratio 2 : 1 2:1 2 : 1 )

VHF/UHF Bands ( > 30 MHz > 30\text{ MHz} > 30 MHz ) 5.0 μ V 5.0\ \mu\text{V} 5.0 μ V − 93.0 dBm -93.0\text{ dBm} − 93.0 dBm 6.0 dB 6.0\text{ dB} 6.0 dB per S-unit (Voltage ratio 2 : 1 2:1 2 : 1 )

The Mathematical Derivation of S9 on HF

Power into a matched 50.0 Ω 50.0\ \Omega 50.0 Ω load is calculated from RMS voltage by P = V 2 / R P = V^2 / R P = V 2 / R : P = ( 50.0 × 10 − 6 V ) 2 50.0 Ω = 2.5 × 10 − 9 50 = 5.0 × 10 − 11 W = 50 pW P = \frac{(50.0 \times 10^{-6}\text{ V})^2}{50.0\ \Omega} = \frac{2.5 \times 10^{-9}}{50} = 5.0 \times 10^{-11}\text{ W} = 50\text{ pW} P = 50.0 Ω ( 50.0 × 1 0 − 6 V ) 2 ​ = 50 2.5 × 1 0 − 9 ​ = 5.0 × 1 0 − 11 W = 50 pW

Converting to dBm \text{dBm} dBm : P (dBm) = 10 log ⁡ 10 ( 5.0 × 10 − 11 W 10 − 3 W ) = 10 log ⁡ 10 ( 5.0 × 10 − 8 ) = 10 × ( − 7.301 ) = − 73.0 dBm P\text{ (dBm)} = 10 \log_{10}\left( \frac{5.0 \times 10^{-11}\text{ W}}{10^{-3}\text{ W}} \right) = 10 \log_{10}(5.0 \times 10^{-8}) = 10 \times (-7.301) = \mathbf{-73.0\text{ dBm}} P (dBm) = 10 lo g 10 ​ ( 1 0 − 3 W 5.0 × 1 0 − 11 W ​ ) = 10 lo g 10 ​ ( 5.0 × 1 0 − 8 ) = 10 × ( − 7.301 ) = − 73.0 dBm

S-Meter Scale Progression on HF

Each S-unit represents exactly a 6 dB 6\text{ dB} 6 dB step (a 2 : 1 2:1 2 : 1 ratio in voltage, or a 4 : 1 4:1 4 : 1 ratio in power):

• S 9 = − 73 dBm S9 = -73\text{ dBm} S 9 = − 73 dBm ( 50.0 μ V 50.0\ \mu\text{V} 50.0 μ V )
• S 8 = − 79 dBm S8 = -79\text{ dBm} S 8 = − 79 dBm ( 25.0 μ V 25.0\ \mu\text{V} 25.0 μ V )
• S 7 = − 85 dBm S7 = -85\text{ dBm} S 7 = − 85 dBm ( 12.5 μ V 12.5\ \mu\text{V} 12.5 μ V )
• S 6 = − 91 dBm S6 = -91\text{ dBm} S 6 = − 91 dBm ( 6.25 μ V 6.25\ \mu\text{V} 6.25 μ V )
• S 5 = − 97 dBm S5 = -97\text{ dBm} S 5 = − 97 dBm ( 3.12 μ V 3.12\ \mu\text{V} 3.12 μ V )
• S 4 = − 103 dBm S4 = -103\text{ dBm} S 4 = − 103 dBm ( 1.56 μ V 1.56\ \mu\text{V} 1.56 μ V )
• S 3 = − 109 dBm S3 = -109\text{ dBm} S 3 = − 109 dBm ( 0.78 μ V 0.78\ \mu\text{V} 0.78 μ V )
• S 2 = − 115 dBm S2 = -115\text{ dBm} S 2 = − 115 dBm ( 0.39 μ V 0.39\ \mu\text{V} 0.39 μ V )
• S 1 = − 121 dBm S1 = -121\text{ dBm} S 1 = − 121 dBm ( 0.20 μ V 0.20\ \mu\text{V} 0.20 μ V )

Signals above S 9 S9 S 9 are read directly in decibels above the S 9 S9 S 9 reference: S 9 + 10 dB S9 + 10\text{ dB} S 9 + 10 dB ( − 63 dBm -63\text{ dBm} − 63 dBm ) , S 9 + 20 dB S9 + 20\text{ dB} S 9 + 20 dB ( − 53 dBm -53\text{ dBm} − 53 dBm ) , up to S 9 + 60 dB S9 + 60\text{ dB} S 9 + 60 dB ( − 13 dBm -13\text{ dBm} − 13 dBm ) .

5. Comparing Receiver Specifications

Compare measurements made under the same conditions. A product tier or one impressive number does not establish performance on every band or at every signal spacing.

Metric Conditions that must accompany it How to interpret it

MDS Frequency, equivalent noise bandwidth, preamp/attenuator settings Lower input power means better noise-limited sensitivity under those conditions.

Noise figure Frequency and the same gain configuration Relate it to MDS using − 174 + 10 log ⁡ 10 ( B ) + N F -174+10\log_{10}(B)+NF − 174 + 10 lo g 10 ​ ( B ) + NF at 290 K 290\text{ K} 290 K .

IMD3 dynamic range Per-tone levels, tone spacing, bandwidth, gain settings Indicates resistance to two-tone third-order products; compare equal test conditions.

Blocking dynamic range Interferer spacing, AGC condition, bandwidth and 1 dB 1\text{ dB} 1 dB wanted-signal reduction criterion Describes compression/desensitisation, rather than the noise rise measured for RMDR.

RMDR Carrier offset, bandwidth, gain settings and source phase-noise purity Indicates resistance to reciprocal mixing; the test source must not set the observed noise limit.

Roofing filters Available passbands and measured stopband response Narrower filtering can protect later stages; check which earlier stages remain exposed.

Shape factor Both attenuation levels and the selected filter For S F 60 / 6 SF_{60/6} S F 60/6 ​ , divide the 60 dB 60\text{ dB} 60 dB bandwidth by the 6 dB 6\text{ dB} 6 dB bandwidth.

• 6. Worked Engineering Examples
• Worked Example 7.4.1: MDS and Noise Figure in Different Detection Bandwidths

An amateur receiver has N F = 12.0 dB NF=12.0\text{ dB} NF = 12.0 dB with its preamplifier off. Assume a matched 290 K 290\text{ K} 290 K source and equivalent noise bandwidths of 500 Hz 500\text{ Hz} 500 Hz and 2.4 kHz 2.4\text{ kHz} 2.4 kHz .

Calculate the Minimum Discernible Signal (MDS) in a 500 Hz 500\text{ Hz} 500 Hz CW bandwidth : 10 log ⁡ 10 ( 500 ) = 10 × 2.6990 = 26.99 dB 10 \log_{10}(500) = 10 \times 2.6990 = 26.99\text{ dB} 10 lo g 10 ​ ( 500 ) = 10 × 2.6990 = 26.99 dB MDS CW = − 174.0 dBm/Hz + 26.99 dB + 12.0 dB = − 135.01 dBm ≈ − 135.0 dBm \text{MDS}_{\text{CW}} = -174.0\text{ dBm/Hz} + 26.99\text{ dB} + 12.0\text{ dB} = -135.01\text{ dBm} \approx -135.0\text{ dBm} MDS CW ​ = − 174.0 dBm/Hz + 26.99 dB + 12.0 dB = − 135.01 dBm ≈ − 135.0 dBm

Calculate the MDS in a 2.4 kHz 2.4\text{ kHz} 2.4 kHz SSB voice bandwidth : 10 log ⁡ 10 ( 2400 ) = 10 × 3.3802 = 33.80 dB 10 \log_{10}(2400) = 10 \times 3.3802 = 33.80\text{ dB} 10 lo g 10 ​ ( 2400 ) = 10 × 3.3802 = 33.80 dB MDS SSB = − 174.0 dBm/Hz + 33.80 dB + 12.0 dB = − 128.20 dBm \text{MDS}_{\text{SSB}} = -174.0\text{ dBm/Hz} + 33.80\text{ dB} + 12.0\text{ dB} = -128.20\text{ dBm} MDS SSB ​ = − 174.0 dBm/Hz + 33.80 dB + 12.0 dB = − 128.20 dBm

Observation: Switching from SSB ( 2.4 kHz 2.4\text{ kHz} 2.4 kHz ) to CW ( 500 Hz 500\text{ Hz} 500 Hz ) lowers the receiver's thermal noise floor by 33.80 − 26.99 = 6.81 dB 33.80 - 26.99 = 6.81\text{ dB} 33.80 − 26.99 = 6.81 dB —nearly 7 dB 7\text{ dB} 7 dB of sensitivity gain achieved purely by narrowing detection bandwidth!

Convert the CW MDS ( − 135.0 dBm -135.0\text{ dBm} − 135.0 dBm ) into equivalent microvolts ( V RMS V_{\text{RMS}} V RMS ​ ) across 50.0 Ω 50.0\ \Omega 50.0 Ω : P = 10 − 135.0 10 mW = 3.162 × 10 − 14 mW = 3.162 × 10 − 17 W P = 10^{\frac{-135.0}{10}}\text{ mW} = 3.162 \times 10^{-14}\text{ mW} = 3.162 \times 10^{-17}\text{ W} P = 1 0 10 − 135.0 ​ mW = 3.162 × 1 0 − 14 mW = 3.162 × 1 0 − 17 W V RMS = P × R = 3.162 × 10 − 17 W × 50 Ω = 1.581 × 10 − 15 ≈ 3.98 × 10 − 8 V = 0.0398 μ V ≈ 0.04 μ V ! V_{\text{RMS}} = \sqrt{P \times R} = \sqrt{3.162 \times 10^{-17}\text{ W} \times 50\ \Omega} = \sqrt{1.581 \times 10^{-15}} \approx 3.98 \times 10^{-8}\text{ V} = 0.0398\ \mu\text{V} \approx 0.04\ \mu\text{V}! V RMS ​ = P × R ​ = 3.162 × 1 0 − 17 W × 50 Ω ​ = 1.581 × 1 0 − 15 ​ ≈ 3.98 × 1 0 − 8 V = 0.0398 μ V ≈ 0.04 μ V !

Worked Example 7.4.2: Calculating Two-Tone I M D 3 IMD3 I M D 3 Dynamic Range and S-Meter Signal Level

A receiver front-end exhibits a measured Third-Order Input Intercept Point of I I P 3 = + 18.0 dBm IIP_3 = +18.0\text{ dBm} II P 3 ​ = + 18.0 dBm and an MDS of − 138.0 dBm -138.0\text{ dBm} − 138.0 dBm in a 500 Hz 500\text{ Hz} 500 Hz bandwidth.

Calculate the receiver's Two-Tone Third-Order Intermodulation Dynamic Range ( I M D 3 DR IMD3\text{ DR} I M D 3 DR ): I M D 3 DR = 2 3 ( I I P 3 − MDS ) = 2 3 ( + 18.0 dBm − ( − 138.0 dBm ) ) IMD3\text{ DR} = \frac{2}{3} \left( IIP_3 - \text{MDS} \right) = \frac{2}{3} \left( +18.0\text{ dBm} - (-138.0\text{ dBm}) \right) I M D 3 DR = 3 2 ​ ( II P 3 ​ − MDS ) = 3 2 ​ ( + 18.0 dBm − ( − 138.0 dBm ) ) I M D 3 DR = 2 3 ( 156.0 dB ) = 104.0 dB IMD3\text{ DR} = \frac{2}{3} (156.0\text{ dB}) = 104.0\text{ dB} I M D 3 DR = 3 2 ​ ( 156.0 dB ) = 104.0 dB

Calculate the individual power level per tone ( P tone P_{\text{tone}} P tone ​ ) of two equal off-channel interfering signals that will generate third-order IMD products just equal to the receiver noise floor ( − 138.0 dBm -138.0\text{ dBm} − 138.0 dBm ): P tone = MDS + I M D 3 DR = − 138.0 dBm + 104.0 dB = − 34.0 dBm P_{\text{tone}} = \text{MDS} + IMD3\text{ DR} = -138.0\text{ dBm} + 104.0\text{ dB} = -34.0\text{ dBm} P tone ​ = MDS + I M D 3 DR = − 138.0 dBm + 104.0 dB = − 34.0 dBm

Convert − 34.0 dBm -34.0\text{ dBm} − 34.0 dBm to its corresponding S-meter reading on the HF bands:

On HF, S 9 = − 73.0 dBm S9 = -73.0\text{ dBm} S 9 = − 73.0 dBm . The tone power is: P tone − S 9 = − 34.0 dBm − ( − 73.0 dBm ) = + 39.0 dB P_{\text{tone}} - S9 = -34.0\text{ dBm} - (-73.0\text{ dBm}) = +39.0\text{ dB} P tone ​ − S 9 = − 34.0 dBm − ( − 73.0 dBm ) = + 39.0 dB

This corresponds to an immense signal level of S 9 + 39 dB S9 + 39\text{ dB} S 9 + 39 dB ( 4.46 mV 4.46\text{ mV} 4.46 mV )! Two interfering signals must reach S 9 + 39 dB S9 + 39\text{ dB} S 9 + 39 dB before their third-order intermodulation product becomes detectable in the receiver passband.