15.2 Receiver Susceptibility, Desensitisation, and Front-End Intermodulation

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.

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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 $f_{\text{high}}<2f_{\text{low}}$: $3.0$–$5.5\text{ MHz}$ qualifies, whereas $3.0$–$7.5\text{ MHz}$ does not. General coverage or a panoramic display does not by itself establish whether RF preselection is fitted.

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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, $A_v\approx-g_mR_L$ 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 $1\text{ dB}$ compression in the output level of a desired weak signal:

$$\text{BDR (dB)} = P_{1\text{dB}} - \text{MDS}$$

• Noise Reference: At290K and noise bandwidth $B_N$, the input-referred noise is approximately $-174+10\log_{10}(B_N)+\text{NF}$ dBm. With $B_N=500\text{ Hz}$ this is $-147+\text{NF}$ 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.

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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:

$$v_{\text{out}}(t) = a_1 v_{\text{in}}(t) + a_2 v_{\text{in}}^2(t) + a_3 v_{\text{in}}^3(t)$$

Suppose the composite input voltage consists of two signals:

1. A weak, desired carrier at frequency $\omega_d$: $v_d(t) = V_d \cos(\omega_d t)$.
2. An intense, amplitude-modulated unwanted carrier at frequency $\omega_u$: $v_u(t) = V_u [1 + m_u \cos(\omega_m t)] \cos(\omega_u t)$, where $m_u$ is the modulation index and $\omega_m$ is the audio modulating frequency.

Substituting $v_{\text{in}}(t) = v_d(t) + v_u(t)$ into the cubic term $a_3 v_{\text{in}}^3(t)$ yields several cross-product terms. The specific term combining the desired carrier with the square of the unwanted carrier is:

$$v_{\text{cross}}(t) = 3 a_3 v_d(t) v_u^2(t) = 3 a_3 V_d \cos(\omega_d t) \left\{ V_u [1 + m_u \cos(\omega_m t)] \cos(\omega_u t) \right\}^2$$

Expanding the trigonometric identity $\cos^2(\omega_u t) = \frac{1 + \cos(2\omega_u t)}{2}$ and extracting the low-frequency envelope component multiplying the desired carrier:

$$v_{\text{cross}}(t) = \frac{3}{2} a_3 V_d V_u^2 \left[ 1 + 2 m_u \cos(\omega_m t) + m_u^2 \cos^2(\omega_m t) \right] \cos(\omega_d t)$$

Adding this to the linear fundamental component ($a_1 V_d \cos(\omega_d t)$) gives the net signal at the desired carrier frequency $\omega_d$:

$$v_{\text{net}, \omega_d}(t) = a_1 V_d \left\{ 1 + \frac{3 a_3}{2 a_1} V_u^2 \left[ 1 + 2 m_u \cos(\omega_m t) + \dots \right] \right\} \cos(\omega_d t)$$

Identifying Cross-Modulation in Practice

The cubic model predicts that the transferred modulation at $\omega_d$ 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.

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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 ($2f_1 - f_2$ and $2f_2 - f_1$)

Let two strong off-channel signals be present at frequencies $f_1$ and $f_2$ (with $f_2 > f_1$). Within a non-linear device, their interaction generates multiple orders of products:

• Second-Order Products ($f_1+f_2$, $\lvert f_2-f_1\rvert$, $2f_1$, $2f_2$): 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 ($2f_1 - f_2$ and $2f_2 - f_1$): These are extremely dangerous because they appear at frequency separations identical to the spacing between the fundamental signals ($\Delta f = f_2 - f_1$): $$f_{\text{IMD3, lower}} = 2f_1 - f_2 = f_1 - \Delta f$$ $$f_{\text{IMD3, upper}} = 2f_2 - f_1 = f_2 + \Delta f$$ 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 ($\text{IP}_3$)

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 $3\text{ dB}$ product-power change per $1\text{ dB}$ 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 ($\text{IP}_3$):

• Input-Referred Intercept Point ($\text{IIP}_3$): Expressed in $\text{dBm}$ at the antenna input: $$\text{IIP}_3 = P_{\text{in}} + \frac{\Delta \text{IMD}}{2}$$ where $P_{\text{in}}$ is the input power per tone and $\Delta \text{IMD}$ is the difference in decibels between the fundamental output tone and the third-order product.
• Two-Tone Third-Order Dynamic Range ($\text{IMD DR}_3$): $$\text{IMD DR}_3 = \frac{2}{3} (\text{IIP}_3 - \text{MDS})$$ An exceptional HF receiver features an $\text{IIP}_3 \ge +25\text{ to } +35\text{ dBm}$ (preamp off), yielding an $\text{IMD DR}_3 > 105\text{ to }110\text{ dB}$.

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Image Interference and Intermediate Frequency (IF) Breakthrough

Image Interference Mechanics

In a superheterodyne receiver, the RF signal ($f_{\text{sig}}$) is mixed with a local oscillator ($f_{\text{LO}}$) to produce a constant intermediate frequency ($f_{\text{IF}}$):

$$f_{\text{IF}} = |f_{\text{sig}} - f_{\text{LO}}|$$

Because mixers multiply signals indiscriminately, there is always a second frequency—the image frequency ($f_{\text{image}}$)—that produces the exact same intermediate frequency when mixed with $f_{\text{LO}}$:

• For High-Side Injection ($f_{\text{LO}} = f_{\text{sig}} + f_{\text{IF}}$): $$f_{\text{image}} = f_{\text{LO}} + f_{\text{IF}} = f_{\text{sig}} + 2f_{\text{IF}}$$
• For Low-Side Injection ($f_{\text{LO}}=f_{\text{sig}}-f_{\text{IF}}>0$): $$f_{\text{image}}=\lvert f_{\text{LO}}-f_{\text{IF}}\rvert=\lvert f_{\text{sig}}-2f_{\text{IF}}\rvert.$$ If $f_{\text{LO}}>f_{\text{IF}}$, both responses use the difference product. If $f_{\text{LO}}<f_{\text{IF}}$, the positive image instead produces IF through $f_{\text{image}}+f_{\text{LO}}$; its separation from the desired frequency is then not generally $2f_{\text{IF}}$.

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.

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Mitigations at the Receiver

1. RF Step Attenuators (The $10\text{ dB} / 20\text{ dB}$ 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 $3:1$ ratio with input power:

• Inserting a $10\text{ dB}$ attenuator reduces the fundamental input signals by $10\text{ dB}$.
• Crucially, it reduces the third-order IMD products by $30\text{ dB}$!
• The net signal-to-intermodulation distortion ratio improves by $20\text{ dB}$.

2. High-Performance Front-End Preselection

• Sub-Octave Bandpass Filters: For signals both confined to $f_{\text{low}}<f<f_{\text{high}}<2f_{\text{low}}$, 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.

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Step-by-Step Worked Calculations

Worked Example 1: Third-Order Intermodulation and Attenuator Effect

A receiver tuned to $7.050\text{ MHz}$ receives two equal test signals at $7.150$ and $7.250\text{ MHz}$, each at $-20\text{ dBm}$. 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: $\text{IIP}_3 = +15\text{ dBm}$
• Minimum Discernible Signal: $\text{MDS} = -135\text{ dBm}$ ($500\text{ Hz}$ bandwidth)

1. Calculate the frequencies of the two third-order IMD products and verify if either falls within the 40-meter amateur band ($7.000 - 7.300\text{ MHz}$).
2. Calculate the power level of the phantom IMD signal in dBm and compare it to the receiver noise floor (MDS).
3. Calculate the power level of the phantom signal if a $10\text{ dB}$ attenuator is switched in.

Step 1: Calculate the third-order IMD frequencies:

$$f_{\text{IMD3, lower}} = 2f_1 - f_2 = 2(7.150) - 7.250 = 14.300 - 7.250 = 7.050\text{ MHz}$$ $$f_{\text{IMD3, upper}} = 2f_2 - f_1 = 2(7.250) - 7.150 = 14.500 - 7.150 = 7.350\text{ MHz}$$

The lower product ($f_{\text{IMD3, lower}} = 7.050\text{ MHz}$) 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:

$$P_{\text{IMD3}} = 3 P_{\text{in}} - 2 \text{IIP}_3$$

Substitute $P_{\text{in}} = -20\text{ dBm}$ and $\text{IIP}_3 = +15\text{ dBm}$:

$$P_{\text{IMD3}} = 3(-20) - 2(+15) = -60 - 30 = -90\text{ dBm}$$

Compare to the noise floor (MDS):

$$\text{Level above MDS} = P_{\text{IMD3}} - \text{MDS} = -90\text{ dBm} - (-135\text{ dBm}) = 45\text{ dB}$$

The $-90\text{ dBm}$ equivalent input product is45dB above the stated MDS. On the IARU recommended HF calibration, $S9=-73\text{ dBm}$ and $S6=-91\text{ dBm}$, so it is near S6. Actual receiver S-meter behaviour may differ.

Step 3: Calculate the effect of a $10\text{ dB}$ attenuator:

With the $10\text{ dB}$ attenuator inserted, the input power per tone drops to $P_{\text{in, new}} = -20 - 10 = -30\text{ dBm}$:

$$P_{\text{IMD3, new}} = 3(-30) - 2(+15) = -90 - 30 = -120\text{ dBm}$$

The external pad precedes the receiver; it is not an output attenuator. The new $-120\text{ dBm}$ 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.

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Worked Example 2: Image Frequency and Rejection Calculation

An amateur superheterodyne receiver has an intermediate frequency of $f_{\text{IF}} = 9.000\text{ MHz}$ and uses high-side local oscillator injection. The receiver is tuned to $f_{\text{sig}} = 14.200\text{ MHz}$ on the 20-meter band.

1. Calculate the local oscillator frequency ($f_{\text{LO}}$).
2. Calculate the corresponding image frequency ($f_{\text{image}}$).
3. If a commercial transmitter operates at $f_{\text{image}}$ with an antenna terminal power of $P_{\text{image}} = -30\text{ dBm}$, and the receiver's RF preselector provides $55\text{ dB}$ of attenuation at the image frequency, calculate the image signal power reaching the mixer.

Step 1: Calculate the local oscillator frequency:

$$f_{\text{LO}} = f_{\text{sig}} + f_{\text{IF}} = 14.200\text{ MHz} + 9.000\text{ MHz} = 23.200\text{ MHz}$$

Step 2: Calculate the image frequency:

$$f_{\text{image}} = f_{\text{LO}} + f_{\text{IF}} = f_{\text{sig}} + 2f_{\text{IF}} = 14.200\text{ MHz} + 2(9.000\text{ MHz}) = 32.200\text{ MHz}$$

The image lies at $32.200\text{ MHz}$ in the VHF spectrum.

Step 3: Calculate the image power reaching the mixer:

$$P_{\text{image, mixer}} = P_{\text{image}} - \text{Preselector Attenuation} = -30\text{ dBm} - 55\text{ dB} = -85\text{ dBm}$$

Without the preselector's $55\text{ dB}$ attenuation, the $32.200\text{ MHz}$ signal would enter the mixer unhindered and produce an $S9+43\text{ dB}$ interfering signal on $14.200\text{ MHz}$.

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Receiver Overload Artifact Diagnosis Matrix