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15.2 Receiver Susceptibility, Desensitisation, and Front-End Intermodulation
ACMA Amateur Radio Advanced Recognition Certificate - Theory Exam
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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
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15.2 Receiver Susceptibility, Desensitisation, and Front-End Intermodulation
Key Takeaways Explain This Topic AI
Front-end overload and desensitisation (blocking) occur when an intense off-frequency signal drives the receiver's RF preamplifier or first mixer into non-linear gain compression, collapsing sensitivity and rendering weak desired signals unreadable.
Blocking Dynamic Range (BDR) quantifies a receiver's overload immunity, defined as the ratio in decibels between the receiver noise floor (Minimum Discernible Signal, MDS) and the input power of an unwanted off-frequency carrier that produces a 1 dB 1\text{ dB} 1 dB gain compression in a weak target signal.
Cross-modulation is the non-linear transfer of amplitude modulation from a strong unwanted off-frequency carrier onto a desired weak carrier within an active receiver stage, driven by third-order transfer function terms ( a 3 v i 3 a_3 v_i^3 a 3 v i 3 ).
Front-End Intermodulation Distortion (IMD) generates third-order products at 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 from two strong external signals ( f 1 , f 2 f_1, f_2 f 1 , f 2 ); if these phantom frequencies fall inside an amateur allocation, they create spurious signals indistinguishable from real stations.
An attenuator ahead of a weakly nonlinear receiver stage lowers internally generated IMD3 by about 3 dB 3\text{ dB} 3 dB per 1 dB 1\text{ dB} 1 dB input reduction, while wanted signals fall 1 dB 1\text{ dB} 1 dB . RF preselection and suitable high-linearity mixers also help; sensitivity and external-noise dominance determine the useful attenuation.
Last updated: November 2026
15.2 Receiver Susceptibility, Desensitisation, and Front-End Intermodulation
An amateur antenna receives desired signals together with strong broadcast, land-mobile and nearby amateur signals. Excessive levels can cause blocking, cross-modulation, intermodulation or ADC clipping. Image response is a separate conversion ambiguity: it can occur in an otherwise linear mixer system without overload. Effective reception requires both adequate strong-signal handling and appropriate RF/IF selectivity.
Receiver Front-End Architecture and Susceptibility
A modern communication receiver—whether based on a traditional superheterodyne architecture or a direct-sampling Software Defined Radio (SDR)—relies on a series of selective stages to extract microvolt-level signals from the electromagnetic noise floor. Antenna --> attenuator --> RF preselector --> RF amplifier --> mixer
- |
- v
- roofing/IF filter
- |
- v
- later stages / DSP
- The IF filter reduces blockers reaching later stages; RF amplifier and
mixer must tolerate the signals reaching them before that filter.
A direct-sampling receiver instead needs headroom at its ADC input.
Receiver preselection may use a tracking tuned circuit, switched bandpass filters, or a wider input filter appropriate to a sampling receiver. The bandwidth sets which strong signals reach the first vulnerable stage. A sub-octave band has f high < 2 f low f_{\text{high}}<2f_{\text{low}} f high < 2 f low : 3.0 3.0 3.0 – 5.5 MHz 5.5\text{ MHz} 5.5 MHz qualifies, whereas 3.0 3.0 3.0 – 7.5 MHz 7.5\text{ MHz} 7.5 MHz does not. General coverage or a panoramic display does not by itself establish whether RF preselection is fitted.
Front-End Overload and Desensitisation (Blocking)
Desensitisation —commonly referred to as blocking —occurs when an extremely strong signal on an adjacent or off-channel frequency enters the receiver front-end and forces an active stage (the RF preamplifier or the first mixer) into non-linear gain compression .
The Mechanism of Gain Compression
A strong off-channel signal can change an active stage’s incremental gain for a weak wanted signal. Compression may occur in an RF amplifier, mixer or later stage; a sampling receiver can also reach its ADC limit. The threshold depends on the circuit and preceding gain/filtering, not on a universal100mV input.
For a simple common-source or common-emitter voltage stage, A v ≈ − g m R L A_v\approx-g_mR_L A v ≈ − g m R L illustrates why a reduction in incremental transconductance reduces weak-signal gain. The blocking test holds the wanted input constant and increases a separate unwanted signal until the wanted output falls by1dB. Fixed weak wanted signal -----+
- +-- combiner --> receiver --> measure wanted tone
- Variable off-channel blocker -+
Wanted output level (relative dB)
0 ----------------------.
- \
- 1 ------------------------* blocking threshold
- \
- -----------------------------> blocker input power (dBm)
BDR = blocker level at1dB wanted-signal loss minus measured MDS.
Blocking Dynamic Range (BDR)
The industry-standard figure of merit for receiver overload immunity is the Blocking Dynamic Range (BDR) . BDR is defined as the difference in decibels between the receiver's noise floor ( Minimum Discernible Signal, MDS ) and the input power of an unmodulated off-frequency carrier that causes a 1 dB 1\text{ dB} 1 dB compression in the output level of a desired weak signal: BDR (dB) = P 1 dB − MDS \text{BDR (dB)} = P_{1\text{dB}} - \text{MDS} BDR (dB) = P 1 dB − MDS
Noise Reference: At290K and noise bandwidth B N B_N B N , the input-referred noise is approximately − 174 + 10 log 10 ( B N ) + NF -174+10\log_{10}(B_N)+\text{NF} − 174 + 10 lo g 10 ( B N ) + NF dBm. With B N = 500 Hz B_N=500\text{ Hz} B N = 500 Hz this is − 147 + NF -147+\text{NF} − 147 + NF dBm. Use the measured MDS and stated test conditions when calculating BDR.
Spacing Matters: Report blocker offset, mode, bandwidth and preamp/attenuator settings. Close-in tests may also raise the noise through reciprocal mixing of a strong carrier with LO phase noise. That noise-rise limit is distinct from1dB gain compression; a narrow audio measurement can separate the wanted tone from the added noise. Do not label a reciprocal-mixing result as a measured compression threshold.
Cross-Modulation
Cross-modulation is the unwanted transfer of modulation from an intense, modulated out-of-band carrier onto a completely different, unmodulated or weakly modulated desired carrier inside a non-linear receiver stage.
Mathematical Derivation of Cross-Modulation
Consider a non-linear amplifier whose input-output transfer characteristic contains a cubic non-linearity: v out ( t ) = a 1 v in ( t ) + a 2 v in 2 ( t ) + a 3 v in 3 ( t ) v_{\text{out}}(t) = a_1 v_{\text{in}}(t) + a_2 v_{\text{in}}^2(t) + a_3 v_{\text{in}}^3(t) v out ( t ) = a 1 v in ( t ) + a 2 v in 2 ( t ) + a 3 v in 3 ( t )
Suppose the composite input voltage consists of two signals:
A weak, desired carrier at frequency ω d \omega_d ω d : v d ( t ) = V d cos ( ω d t ) v_d(t) = V_d \cos(\omega_d t) v d ( t ) = V d cos ( ω d t ) .
An intense, amplitude-modulated unwanted carrier at frequency ω u \omega_u ω u : v u ( t ) = V u [ 1 + m u cos ( ω m t ) ] cos ( ω u t ) v_u(t) = V_u [1 + m_u \cos(\omega_m t)] \cos(\omega_u t) v u ( t ) = V u [ 1 + m u cos ( ω m t )] cos ( ω u t ) , where m u m_u m u is the modulation index and ω m \omega_m ω m is the audio modulating frequency.
Substituting v in ( t ) = v d ( t ) + v u ( t ) v_{\text{in}}(t) = v_d(t) + v_u(t) v in ( t ) = v d ( t ) + v u ( t ) into the cubic term a 3 v in 3 ( t ) a_3 v_{\text{in}}^3(t) a 3 v in 3 ( t ) yields several cross-product terms. The specific term combining the desired carrier with the square of the unwanted carrier is: v cross ( t ) = 3 a 3 v d ( t ) v u 2 ( t ) = 3 a 3 V d cos ( ω d t ) { V u [ 1 + m u cos ( ω m t ) ] cos ( ω u t ) } 2 v_{\text{cross}}(t) = 3 a_3 v_d(t) v_u^2(t) = 3 a_3 V_d \cos(\omega_d t) \left\{ V_u [1 + m_u \cos(\omega_m t)] \cos(\omega_u t) \right\}^2 v cross ( t ) = 3 a 3 v d ( t ) v u 2 ( t ) = 3 a 3 V d cos ( ω d t ) { V u [ 1 + m u cos ( ω m t )] cos ( ω u t ) } 2
Expanding the trigonometric identity cos 2 ( ω u t ) = 1 + cos ( 2 ω u t ) 2 \cos^2(\omega_u t) = \frac{1 + \cos(2\omega_u t)}{2} cos 2 ( ω u t ) = 2 1 + c o s ( 2 ω u t ) and extracting the low-frequency envelope component multiplying the desired carrier: v cross ( t ) = 3 2 a 3 V d V u 2 [ 1 + 2 m u cos ( ω m t ) + m u 2 cos 2 ( ω m t ) ] cos ( ω d t ) v_{\text{cross}}(t) = \frac{3}{2} a_3 V_d V_u^2 \left[ 1 + 2 m_u \cos(\omega_m t) + m_u^2 \cos^2(\omega_m t) \right] \cos(\omega_d t) v cross ( t ) = 2 3 a 3 V d V u 2 [ 1 + 2 m u cos ( ω m t ) + m u 2 cos 2 ( ω m t ) ] cos ( ω d t )
Adding this to the linear fundamental component ( a 1 V d cos ( ω d t ) a_1 V_d \cos(\omega_d t) a 1 V d cos ( ω d t ) ) gives the net signal at the desired carrier frequency ω d \omega_d ω d : v net , ω d ( t ) = a 1 V d { 1 + 3 a 3 2 a 1 V u 2 [ 1 + 2 m u cos ( ω m t ) + … ] } cos ( ω d t ) v_{\text{net}, \omega_d}(t) = a_1 V_d \left\{ 1 + \frac{3 a_3}{2 a_1} V_u^2 \left[ 1 + 2 m_u \cos(\omega_m t) + \dots \right] \right\} \cos(\omega_d t) v net , ω d ( t ) = a 1 V d { 1 + 2 a 1 3 a 3 V u 2 [ 1 + 2 m u cos ( ω m t ) + … ] } cos ( ω d t )
Important
The mathematical result proves that the desired carrier ( ω d \omega_d ω d ) is now amplitude-modulated by the audio program ( ω m \omega_m ω m ) of the unwanted transmitter . The cross-modulation depth is proportional to the square of the unwanted signal's amplitude ( V u 2 V_u^2 V u 2 ) and the third-order non-linear coefficient ( a 3 a_3 a 3 ).
Identifying Cross-Modulation in Practice
The cubic model predicts that the transferred modulation at ω d \omega_d ω d depends on the desired carrier:
Carrier Dependence: With unwanted AM maintained at constant level, removing the desired carrier removes this particular cross-modulation product.
Controlled Test: Disappearance of unwanted audio when the desired carrier is removed is consistent with cross-modulation. Keep receiver gain and muting settings fixed, and compare each source alone with both present. A listening observation alone does not uniquely prove which internal mechanism produced the audio.
Front-End Intermodulation Distortion (Receiver IMD)
When two or more intense external signals enter a non-linear receiver stage simultaneously, they mix together to generate intermodulation products . If these generated frequencies coincide with an amateur band, they manifest as phantom signals appearing at frequencies where no actual transmitter exists. Third-order intercept: extrapolate the linear-region level laws.
Fundamental output increases1dB per1dB increase of input per tone.
IMD3 output increases3dB per1dB increase of input per tone.
Their extrapolated intersection is OIP3; IIP3 = OIP3 - gain.
The receiver normally compresses before reaching that theoretical point.
Frequency spectrum (equal spacing Delta=f2-f1):
- IMD3 wanted wanted IMD3
- | | | |
- -----2f1-f2------------f1---------------f2-------------2f2-f1------>
- <---Delta---> <----Delta----> <----Delta---->
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 )
Let two strong off-channel signals be present at frequencies f 1 f_1 f 1 and f 2 f_2 f 2 (with f 2 > f 1 f_2 > f_1 f 2 > f 1 ). Within a non-linear device, their interaction generates multiple orders of products:
Second-Order Products ( f 1 + f 2 f_1+f_2 f 1 + f 2 , ∣ f 2 − f 1 ∣ \lvert f_2-f_1\rvert ∣ f 2 − f 1 ∣ , 2 f 1 2f_1 2 f 1 , 2 f 2 2f_2 2 f 2 ): They are farther from the generating tones than the close-in IMD3 products. Whether they fall in the wanted band depends on both input frequencies. Sub-octave preselection limits which tones reach the nonlinear stage; it cannot remove an in-band product already generated upstream.
Third-Order 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 ): These are extremely dangerous because they appear at frequency separations identical to the spacing between the fundamental signals ( Δ f = f 2 − f 1 \Delta f = f_2 - f_1 Δ f = f 2 − f 1 ): f IMD3, lower = 2 f 1 − f 2 = f 1 − Δ f f_{\text{IMD3, lower}} = 2f_1 - f_2 = f_1 - \Delta f f IMD3, lower = 2 f 1 − f 2 = f 1 − Δ f f IMD3, upper = 2 f 2 − f 1 = f 2 + Δ f f_{\text{IMD3, upper}} = 2f_2 - f_1 = f_2 + \Delta f f IMD3, upper = 2 f 2 − f 1 = f 2 + Δ f If two powerful international shortwave broadcast stations transmit just above an amateur band, their third-order difference product can land directly inside the amateur band, sounding like an authentic, fully modulated transmission.
The Third-Order Intercept Point ( IP 3 \text{IP}_3 IP 3 )
In the weakly nonlinear cubic region, IMD3 voltage amplitude is proportional to the cube of input voltage. Its power is therefore proportional to the cube of input power, giving a 3 dB 3\text{ dB} 3 dB product-power change per 1 dB 1\text{ dB} 1 dB input-power change. This approximation does not continue through compression or ADC clipping.
If the linear response and the third-order response curves are mathematically extrapolated upward, they intersect at a theoretical point called the Third-Order Intercept Point ( IP 3 \text{IP}_3 IP 3 ) :
Input-Referred Intercept Point ( IIP 3 \text{IIP}_3 IIP 3 ): Expressed in dBm \text{dBm} dBm at the antenna input: IIP 3 = P in + Δ IMD 2 \text{IIP}_3 = P_{\text{in}} + \frac{\Delta \text{IMD}}{2} IIP 3 = P in + 2 Δ IMD where P in P_{\text{in}} P in is the input power per tone and Δ IMD \Delta \text{IMD} Δ IMD is the difference in decibels between the fundamental output tone and the third-order product.
Two-Tone Third-Order Dynamic Range ( IMD DR 3 \text{IMD DR}_3 IMD DR 3 ): IMD DR 3 = 2 3 ( IIP 3 − MDS ) \text{IMD DR}_3 = \frac{2}{3} (\text{IIP}_3 - \text{MDS}) IMD DR 3 = 3 2 ( IIP 3 − MDS ) An exceptional HF receiver features an IIP 3 ≥ + 25 to + 35 dBm \text{IIP}_3 \ge +25\text{ to } +35\text{ dBm} IIP 3 ≥ + 25 to + 35 dBm (preamp off), yielding an IMD DR 3 > 105 to 110 dB \text{IMD DR}_3 > 105\text{ to }110\text{ dB} IMD DR 3 > 105 to 110 dB .
- Image Interference and Intermediate Frequency (IF) Breakthrough
- Image Interference Mechanics
In a superheterodyne receiver, the RF signal ( f sig f_{\text{sig}} f sig ) is mixed with a local oscillator ( f LO f_{\text{LO}} f LO ) to produce a constant intermediate frequency ( f IF f_{\text{IF}} f IF ): f IF = ∣ f sig − f LO ∣ f_{\text{IF}} = |f_{\text{sig}} - f_{\text{LO}}| f IF = ∣ f sig − f LO ∣
Because mixers multiply signals indiscriminately, there is always a second frequency—the image frequency ( f image f_{\text{image}} f image )—that produces the exact same intermediate frequency when mixed with f LO f_{\text{LO}} f LO :
For High-Side Injection ( f LO = f sig + f IF f_{\text{LO}} = f_{\text{sig}} + f_{\text{IF}} f LO = f sig + f IF ): f image = f LO + f IF = f sig + 2 f IF f_{\text{image}} = f_{\text{LO}} + f_{\text{IF}} = f_{\text{sig}} + 2f_{\text{IF}} f image = f LO + f IF = f sig + 2 f IF
For Low-Side Injection ( f LO = f sig − f IF > 0 f_{\text{LO}}=f_{\text{sig}}-f_{\text{IF}}>0 f LO = f sig − f IF > 0 ): f image = ∣ f LO − f IF ∣ = ∣ f sig − 2 f IF ∣ . f_{\text{image}}=\lvert f_{\text{LO}}-f_{\text{IF}}\rvert=\lvert f_{\text{sig}}-2f_{\text{IF}}\rvert. f image = ∣ f LO − f IF ∣ = ∣ f sig − 2 f IF ∣ . If f LO > f IF f_{\text{LO}}>f_{\text{IF}} f LO > f IF , both responses use the difference product. If f LO < f IF f_{\text{LO}}<f_{\text{IF}} f LO < f IF , the positive image instead produces IF through f image + f LO f_{\text{image}}+f_{\text{LO}} f image + f LO ; its separation from the desired frequency is then not generally 2 f IF 2f_{\text{IF}} 2 f IF .
Caution
For ordinary positive-frequency difference responses of one real mixer, the desired signal and image lie on opposite sides of the LO, separated by 2 f IF 2f_{\text{IF}} 2 f IF . Once combined into the same real IF response they cannot be separated by its IF filter; RF preselection must reject the image beforehand. An I/Q image-reject architecture instead preserves phase information for cancellation.
Intermediate Frequency (IF) Breakthrough
IF breakthrough occurs when an external signal at the receiver IF reaches the IF circuitry without the intended conversion/selectivity. An antenna-input IF trap can reject a signal entering through that connector. If it instead couples through enclosure seams, power or other cables directly into the IF stages, improve shielding, bonding and filtering on that path; an antenna trap cannot cure a path that bypasses it. The interference can remain as the tuning dial is moved.
- Mitigations at the Receiver
- 1. RF Step Attenuators (The 10 dB / 20 dB 10\text{ dB} / 20\text{ dB} 10 dB /20 dB Rule)
When operating in high-signal environments, the simplest and most effective tool for curing receiver overload is the front-end RF attenuator . Attenuator Effect on Third-Order IMD
Without Attenuator: With 10 dB Attenuator Inserted:
- Desired Carrier: -30 dBm Desired Carrier: -40 dBm (Drops 10 dB)
- IMD3 Phantom: -60 dBm IMD3 Phantom: -90 dBm (Drops 30 dB!)
- ───────────────────────── ─────────────────────────
- Signal-to-IMD: 30 dB Signal-to-IMD: 50 dB (20 dB IMPROVEMENT!)
Because third-order intermodulation products scale at a 3 : 1 3:1 3 : 1 ratio with input power:
Inserting a 10 dB 10\text{ dB} 10 dB attenuator reduces the fundamental input signals by 10 dB 10\text{ dB} 10 dB .
Crucially, it reduces the third-order IMD products by 30 dB 30\text{ dB} 30 dB !
The net signal-to-intermodulation distortion ratio improves by 20 dB 20\text{ dB} 20 dB .
Note
SNR Tradeoff: On many HF paths, received external noise is well above receiver-added noise. Attenuation then reduces wanted signal and external noise together, with little SNR penalty while improving overload performance. If the attenuated external noise approaches receiver-added noise, SNR deteriorates. Use only the attenuation needed; do not assume every HF path tolerates10dB without loss.
2. High-Performance Front-End Preselection
Sub-Octave Bandpass Filters: For signals both confined to f low < f < f high < 2 f low f_{\text{low}}<f<f_{\text{high}}<2f_{\text{low}} f low < f < f high < 2 f low , their second harmonics/sums lie above that band and their differences below it. Filtering before a nonlinear stage limits the inputs that can generate in-band second-order products. Finite stopband rejection still allows sufficiently strong outside signals through; it does not remove an in-band product generated earlier.
Tuned Preselectors: A narrow RF passband can reject blockers before the first active stage. Required bandwidth follows the wanted signal and tuning range; rejection and insertion loss must be checked at the actual frequencies.
Broadcast Rejection: For HF reception above Medium Wave, use a suitable high-pass filter or a band-stop filter covering the interfering broadcast frequencies. A low-pass filter that passes Medium Wave would not serve this purpose. Verify rejection at the blocker frequencies and acceptable loss on the wanted band.
3. High-Level Passive and Switching Mixers
Receiver designers may use active, passive diode-ring or FET switching mixers, balancing conversion gain/loss, noise and strong-signal handling. High-level diode mixers need the specified LO drive; that rating is not itself an IIP3 guarantee. H-mode switching mixers can achieve high linearity, but switch resistance, drive, balance and terminations still produce finite distortion. Compare measured IIP3 and compression performance at the actual frequencies and operating conditions.
- Step-by-Step Worked Calculations
- Worked Example 1: Third-Order Intermodulation and Attenuator Effect
A receiver tuned to 7.050 MHz 7.050\text{ MHz} 7.050 MHz receives two equal test signals at 7.150 7.150 7.150 and 7.250 MHz 7.250\text{ MHz} 7.250 MHz , each at − 20 dBm -20\text{ dBm} − 20 dBm . Model its weakly nonlinear response with the following input-referred specifications, measured at the receiver connector. A separate external input pad can then be inserted ahead of that connector:
Input Third-Order Intercept Point: IIP 3 = + 15 dBm \text{IIP}_3 = +15\text{ dBm} IIP 3 = + 15 dBm
Minimum Discernible Signal: MDS = − 135 dBm \text{MDS} = -135\text{ dBm} MDS = − 135 dBm ( 500 Hz 500\text{ Hz} 500 Hz bandwidth)
Calculate the frequencies of the two third-order IMD products and verify if either falls within the 40-meter amateur band ( 7.000 − 7.300 MHz 7.000 - 7.300\text{ MHz} 7.000 − 7.300 MHz ).
Calculate the power level of the phantom IMD signal in dBm and compare it to the receiver noise floor (MDS).
Calculate the power level of the phantom signal if a 10 dB 10\text{ dB} 10 dB attenuator is switched in.
Step 1: Calculate the third-order IMD frequencies: f IMD3, lower = 2 f 1 − f 2 = 2 ( 7.150 ) − 7.250 = 14.300 − 7.250 = 7.050 MHz f_{\text{IMD3, lower}} = 2f_1 - f_2 = 2(7.150) - 7.250 = 14.300 - 7.250 = 7.050\text{ MHz} f IMD3, lower = 2 f 1 − f 2 = 2 ( 7.150 ) − 7.250 = 14.300 − 7.250 = 7.050 MHz f IMD3, upper = 2 f 2 − f 1 = 2 ( 7.250 ) − 7.150 = 14.500 − 7.150 = 7.350 MHz f_{\text{IMD3, upper}} = 2f_2 - f_1 = 2(7.250) - 7.150 = 14.500 - 7.150 = 7.350\text{ MHz} f IMD3, upper = 2 f 2 − f 1 = 2 ( 7.250 ) − 7.150 = 14.500 − 7.150 = 7.350 MHz
The lower product ( f IMD3, lower = 7.050 MHz f_{\text{IMD3, lower}} = 7.050\text{ MHz} f IMD3, lower = 7.050 MHz ) falls directly on the tuned frequency inside the 40-meter band.
Step 2: Calculate the power of the phantom signal:
For the weakly nonlinear cubic model, the internally generated product can be expressed as an equivalent input level at the receiver connector: P IMD3 = 3 P in − 2 IIP 3 P_{\text{IMD3}} = 3 P_{\text{in}} - 2 \text{IIP}_3 P IMD3 = 3 P in − 2 IIP 3
Substitute P in = − 20 dBm P_{\text{in}} = -20\text{ dBm} P in = − 20 dBm and IIP 3 = + 15 dBm \text{IIP}_3 = +15\text{ dBm} IIP 3 = + 15 dBm : P IMD3 = 3 ( − 20 ) − 2 ( + 15 ) = − 60 − 30 = − 90 dBm P_{\text{IMD3}} = 3(-20) - 2(+15) = -60 - 30 = -90\text{ dBm} P IMD3 = 3 ( − 20 ) − 2 ( + 15 ) = − 60 − 30 = − 90 dBm
Compare to the noise floor (MDS): Level above MDS = P IMD3 − MDS = − 90 dBm − ( − 135 dBm ) = 45 dB \text{Level above MDS} = P_{\text{IMD3}} - \text{MDS} = -90\text{ dBm} - (-135\text{ dBm}) = 45\text{ dB} Level above MDS = P IMD3 − MDS = − 90 dBm − ( − 135 dBm ) = 45 dB
The − 90 dBm -90\text{ dBm} − 90 dBm equivalent input product is45dB above the stated MDS. On the IARU recommended HF calibration, S 9 = − 73 dBm S9=-73\text{ dBm} S 9 = − 73 dBm and S 6 = − 91 dBm S6=-91\text{ dBm} S 6 = − 91 dBm , so it is near S6. Actual receiver S-meter behaviour may differ.
Step 3: Calculate the effect of a 10 dB 10\text{ dB} 10 dB attenuator:
With the 10 dB 10\text{ dB} 10 dB attenuator inserted, the input power per tone drops to P in, new = − 20 − 10 = − 30 dBm P_{\text{in, new}} = -20 - 10 = -30\text{ dBm} P in, new = − 20 − 10 = − 30 dBm : P IMD3, new = 3 ( − 30 ) − 2 ( + 15 ) = − 90 − 30 = − 120 dBm P_{\text{IMD3, new}} = 3(-30) - 2(+15) = -90 - 30 = -120\text{ dBm} P IMD3, new = 3 ( − 30 ) − 2 ( + 15 ) = − 90 − 30 = − 120 dBm
The external pad precedes the receiver; it is not an output attenuator. The new − 120 dBm -120\text{ dBm} − 120 dBm result is the equivalent product at the same receiver connector used for its IIP3 and MDS. The product has fallen30dB but remains15dB above MDS, so it may still be audible. A wanted external signal falls10dB, improving its ratio to this product by20dB. Referring the result back before the external pad would add10dB to both equivalent product and receiver noise reference.
Worked Example 2: Image Frequency and Rejection Calculation
An amateur superheterodyne receiver has an intermediate frequency of f IF = 9.000 MHz f_{\text{IF}} = 9.000\text{ MHz} f IF = 9.000 MHz and uses high-side local oscillator injection . The receiver is tuned to f sig = 14.200 MHz f_{\text{sig}} = 14.200\text{ MHz} f sig = 14.200 MHz on the 20-meter band.
Calculate the local oscillator frequency ( f LO f_{\text{LO}} f LO ).
Calculate the corresponding image frequency ( f image f_{\text{image}} f image ).
If a commercial transmitter operates at f image f_{\text{image}} f image with an antenna terminal power of P image = − 30 dBm P_{\text{image}} = -30\text{ dBm} P image = − 30 dBm , and the receiver's RF preselector provides 55 dB 55\text{ dB} 55 dB of attenuation at the image frequency, calculate the image signal power reaching the mixer.
Step 1: Calculate the local oscillator frequency: f LO = f sig + f IF = 14.200 MHz + 9.000 MHz = 23.200 MHz f_{\text{LO}} = f_{\text{sig}} + f_{\text{IF}} = 14.200\text{ MHz} + 9.000\text{ MHz} = 23.200\text{ MHz} f LO = f sig + f IF = 14.200 MHz + 9.000 MHz = 23.200 MHz
Step 2: Calculate the image frequency: f image = f LO + f IF = f sig + 2 f IF = 14.200 MHz + 2 ( 9.000 MHz ) = 32.200 MHz f_{\text{image}} = f_{\text{LO}} + f_{\text{IF}} = f_{\text{sig}} + 2f_{\text{IF}} = 14.200\text{ MHz} + 2(9.000\text{ MHz}) = 32.200\text{ MHz} f image = f LO + f IF = f sig + 2 f IF = 14.200 MHz + 2 ( 9.000 MHz ) = 32.200 MHz
The image lies at 32.200 MHz 32.200\text{ MHz} 32.200 MHz in the VHF spectrum.
Step 3: Calculate the image power reaching the mixer: P image, mixer = P image − Preselector Attenuation = − 30 dBm − 55 dB = − 85 dBm P_{\text{image, mixer}} = P_{\text{image}} - \text{Preselector Attenuation} = -30\text{ dBm} - 55\text{ dB} = -85\text{ dBm} P image, mixer = P image − Preselector Attenuation = − 30 dBm − 55 dB = − 85 dBm
Without the preselector's 55 dB 55\text{ dB} 55 dB attenuation, the 32.200 MHz 32.200\text{ MHz} 32.200 MHz signal would enter the mixer unhindered and produce an S 9 + 43 dB S9+43\text{ dB} S 9 + 43 dB interfering signal on 14.200 MHz 14.200\text{ MHz} 14.200 MHz .
Receiver Overload Artifact Diagnosis Matrix
Overload Phenomenon Underlying Physical Mechanism Diagnostic Confirmation Test Key Audio / Operational Signature Most Effective Technical Mitigation
Desensitisation (Blocking) Active stage gain compression ( g m g_m g m collapse) from strong off-channel carrier Tune receiver to weak signal; when strong off-frequency station transmits, weak signal drops or vanishes Background band noise drops abruptly ("goes dead"); S-meter may plunge or lock Insert 10 to 20 dB 10\text{ to }20\text{ dB} 10 to 20 dB front-end attenuator; switch off preamplifier; add high-Q preselector
Cross-Modulation Unwanted AM transferred onto a desired carrier through nonlinearity With fixed gain/unmuted audio, compare both sources against each alone Unwanted modulation at the desired frequency depends on the desired carrier in the cubic model Reduce blocker levels before the nonlinear stage with attenuation or suitable RF filtering
Intermodulation Distortion (IMD) Nonlinear mixing of strong off-channel signals A pad ahead of the responsible stage reduces a cubic IMD3 product about3dB per1dB input change A false response disappears when either generating signal is removed Reduce blocker levels; improve preselection or stage linearity; check the result above the noise floor
Image Interference Another RF frequency converts to the same IF Calculate both possible positive-frequency mixer responses for the actual LO/IF An unwanted station is received at the desired tuning setting; overload is not required Improve RF preselection or use an image-reject architecture
IF Breakthrough An external IF-frequency signal reaches IF circuitry without intended conversion Compare antenna termination, cable paths and source on/off tests Response can persist as the receiver is tuned Use an IF trap for antenna-path ingress; repair shielding/bonding or filter the actual bypass path