Distortion and Intermodulation
A perfect amplifier would reproduce its input signal exactly, only larger. Real amplifiers do not. Every transistor has a non-linear transfer characteristic — the relationship between input voltage and output current is not a straight line. That non-linearity creates distortion: the output contains frequency components that were not in the input. In a receiver, distortion generates phantom signals that appear on frequencies you are trying to receive. In a transmitter, distortion creates harmonics and spurious emissions that cause interference and may violate your licence conditions.
There are two categories of distortion that every ham radio operator needs to understand: harmonic distortion, where a single sine wave at frequency f creates outputs at 2f, 3f, 4f…; and intermodulation distortion (IMD), where two or more signals at different frequencies mix inside the amplifier to create output products at new frequencies — frequencies that can land directly on a signal you are trying to receive. Of these, IMD is more dangerous in modern ham radio practice because it cannot be filtered away at the amplifier output: the spurious products are within the receiver's passband.
Why Amplifiers Distort
The collector current of a BJT transistor obeys the diode equation: IC = IS × e^(VBE/VT), where VT = 26 mV at room temperature. This exponential relationship is highly non-linear. For small signals around the Q-point, the transistor's transfer curve is approximately linear — that approximation is what makes small-signal amplifier analysis work. But as signal amplitude increases, the non-linearity becomes significant, and the output is no longer a faithful replica of the input.
Mathematically, any non-linear function can be expressed as a Taylor series expansion around its operating point:
The first term (a₁·vin) is the desired linear amplification. The higher-order terms create distortion products:
- The a₂ (second-order) term generates distortion at DC and at twice the input frequency (2f).
- The a₃ (third-order) term generates distortion at the input frequency (gaining it slightly — called gain compression) and at three times the input frequency (3f).
- When two tones at f1 and f2 are present, the a₂ term mixes them to produce products at f1±f2, and the a₃ term produces products at 2f1−f2 and 2f2−f1.
The third-order products (2f1−f2 and 2f2−f1) are critically important because when f1 and f2 are close together — as is normal in a crowded ham band — these products fall very close to f1 and f2, inside the receiver's passband where no filter can remove them.
Harmonic Distortion and THD
When a single sine wave at frequency f is amplified by a non-linear amplifier, the output contains the fundamental at f plus harmonics at 2f, 3f, 4f, and so on. The amplitude of each harmonic relative to the fundamental is the harmonic distortion figure:
Third harmonic distortion (HD3) = V3f / Vf × 100%
Total Harmonic Distortion (THD) = √(V₂f² + V₃f² + V₄f² + …) / Vf × 100%
For audio amplifiers, THD is the standard quality metric. A high-fidelity audio amplifier might have THD < 0.1%. A speech processing amplifier in a transceiver might have THD of 1–3% at full output — audible but acceptable for SSB voice. A Class C RF power amplifier might have THD of 20% or more, but its tank circuit filter removes the harmonics before they reach the antenna.
Harmonics from a transmitter are a regulatory concern. The ITU and national regulators specify maximum harmonic and spurious emission levels. For example, the FCC requires that harmonics from amateur transmitters above 30 MHz be at least 43 dB below the carrier (and at least 50 μW). Harmonics at 2f and 3f from a 7 MHz (40-metre) transmitter fall at 14 MHz and 21 MHz — right in the 20-metre and 15-metre ham bands, potentially interfering with other stations.
Intermodulation Distortion
When two or more signals at different frequencies pass through a non-linear amplifier simultaneously, they mix together to produce intermodulation products at frequencies that are sums and differences of integer multiples of the input frequencies.
For two input tones at f1 and f2, the intermodulation products are at:
Third-order products: 2f1 − f2 and 2f2 − f1 (close to f1 and f2 — dangerous)
Fifth-order products: 3f1 − 2f2 and 3f2 − 2f1 (slightly further away)
The second-order products fall at f1+f2 (above both tones) and f1−f2 (below both tones, often in or near the audio range for an RF receiver). They are problematic in wideband amplifiers without input filtering — an amplifier covering 1–30 MHz with no input filter can receive second-order products from AM broadcast stations (500 kHz–1600 kHz) mixing to produce false signals in the HF ham bands.
The third-order products at 2f1−f2 and 2f2−f1 are the most damaging in narrowband ham radio. If f1 = 14.200 MHz and f2 = 14.210 MHz (two SSB stations 10 kHz apart on 20 metres), the third-order products appear at 14.190 MHz and 14.220 MHz — right next to both stations, inside any reasonable IF filter passband. These spurious signals cannot be filtered away after the fact.
The Two-Tone Test
The two-tone test is the standard measurement method for IMD in SSB and linear amplifiers. Two equal-amplitude sine wave tones are applied simultaneously to the amplifier input — typically at audio frequencies of 700 Hz and 1900 Hz for SSB testing, or at two RF frequencies separated by a few kilohertz for RF amplifier testing. The output spectrum is examined on a spectrum analyser to measure the amplitude of the IM products relative to the desired tones.
The result is reported as the IMD ratio, typically in dBc (decibels below carrier):
For example, if the third-order IM product is 40 dB below each tone, the IMD is −40 dBc. For ham radio SSB transmitters, the ARRL recommends IMD ≤ −30 dBc and excellent transmitters achieve −40 dBc or better. A transmitter with only −20 dBc IMD will produce audible splatter — distortion products that extend beyond the intended bandwidth and interfere with adjacent channels.
Third-Order Intercept Point (IP3)
As input signal power increases, the third-order IM products grow faster than the desired output — specifically, for every 1 dB increase in each input tone, the third-order products increase by 3 dB. If you plot both curves on a log-log scale (power in dBm vs. power in dBm), the desired output curve has a slope of 1 and the third-order product curve has a slope of 3. If extended far beyond where the amplifier actually saturates, these two lines would intersect at a theoretical point called the third-order intercept point (IP3).
Output IP3 (OIP3): OIP3 = IIP3 + gain (in dB)
Relationship to IMD ratio:
IMD3 (dBc) = 2 × (IIP3 − Pin)
or equivalently:
IIP3 = Pin + |IMD₃| / 2
The IP3 point is never actually reached — the amplifier clips or saturates well before that power level. But IP3 is an extremely useful figure of merit because it predicts how strong interfering signals must be before they generate IM products at a given level in the receiver.
A receiver front end is tested with two equal tones at −30 dBm each. The third-order IM products are measured at −90 dBm each. What is IIP3?
IMD₃ = −90 dBm − (−30 dBm) = −60 dBc
IIP3 = Pin + |IMD₃| / 2 = −30 + 60/2 = −30 + 30 = 0 dBm
Answer: IIP3 = 0 dBm
This is a typical figure for a good BJT preamplifier on HF. A MOSFET or cascode preamplifier might achieve IIP3 = +10 to +20 dBm. A direct-conversion SDR receiver front end might have IIP3 = −10 dBm, which explains why strong broadcast stations can create spurious signals in SDR receivers.
The 1 dB Compression Point
As signal level rises, the amplifier's gain begins to decrease — a phenomenon called gain compression. This is caused by the transistor spending more time near the edges of its linear region (near cutoff or saturation). The 1 dB compression point (P1dB) is the input power at which the actual gain has fallen 1 dB below the small-signal gain. It is a practical limit: above P1dB the amplifier is clearly non-linear and generates significant distortion.
IIP3 ≈ P1dB + 10 dB
This 10 dB rule of thumb is a useful approximation for BJT and JFET amplifiers. For a receiver front end with IIP3 = 0 dBm, P1dB ≈ −10 dBm. Signals stronger than −10 dBm at the receiver input will cause compression and significant IMD. In a typical ham station, a nearby transmitter at 100 W (50 dBm at the antenna) attenuated by 60 dB of path loss arrives at −10 dBm — right at the compression point of a preamplifier with IIP3 = 0 dBm. This is why high-IP3 preamplifiers matter in contest operation.
Crossover Distortion in Class B
Class B and Class AB amplifiers use two transistors, each conducting for half of the signal cycle. Class B amplifiers have each transistor biased exactly at cutoff — the transistor conducts only when the input drives it into conduction. This means there is a dead zone around zero crossing where neither transistor is conducting, creating a characteristic S-shaped distortion in the output waveform called crossover distortion.
Crossover distortion is prominent in Class B amplifiers and creates high-order harmonics — predominantly odd harmonics (3rd, 5th, 7th) — that give the output a harsh quality. The audio industry largely solved this problem by moving to Class AB operation, where each transistor is biased slightly into conduction so that there is always some transistor conducting at every point of the signal cycle. The crossover region becomes a smooth overlap rather than a dead zone.
In ham radio power amplifiers, Class AB is the standard for SSB and data modes because it provides much lower IMD than Class B while maintaining better efficiency than Class A. Proper crossover bias is critical: too little idle current gives poor IMD (crossover distortion); too much idle current wastes power and causes the transistors to overheat.
Amplifier Class and Distortion
| Class | Conduction Angle | Typical IMD / THD | Distortion Type | Ham Radio Use |
|---|---|---|---|---|
| A | 360° | Lowest — THD <1% at moderate output | Mainly 2nd harmonic (even-order) | Receive preamps, IF amps, audio stages, VFO buffers |
| AB | 180°–360° | Low — IMD typically −30 to −40 dBc | Crossover (if bias too low), else mainly 3rd order | SSB/CW linear power amplifiers, driver stages |
| B | 180° | Moderate — significant crossover distortion | Crossover (odd harmonics) | Rarely used alone; combined with AB correction |
| C | <180° | Very high — THD 20%+ but harmonics filtered | All harmonics; only fundamental passes tank circuit | CW/FM RF power stages with L/C tank output |
| D | Switching | Very low in-band after filtering | Switching transients; filtered by low-pass | Switching power supplies, some SDR applications |
IP3 and IMD Calculator
IP3 and Intermodulation Calculator
Use this calculator in two ways: calculate IP3 from a two-tone test measurement, or predict the IM product level from a known IP3 and input power. Both Input IP3 (IIP3) and Output IP3 (OIP3) are computed. Enter dBm values throughout.
IMD in Ham Radio Practice
The practical consequence of IMD in ham radio is receiver desensitisation and phantom signal generation. Here is how it plays out in a real-world scenario:
You are operating on 14.200 MHz (20 metres, SSB). A strong local station — perhaps a contest station two suburbs away — is transmitting on 14.210 MHz. Another nearby station is on 14.220 MHz. Both arrive at your antenna with substantial power, perhaps −30 dBm each (a very strong HF signal). Your receiver's preamplifier has IIP3 = −5 dBm (a mediocre design). The IMD calculation gives:
f1 = 14.210 MHz, f2 = 14.220 MHz
Input power of each: −30 dBm
IIP3 = −5 dBm (preamplifier)
IMD₃ = 2 × (IIP3 − Pin) = 2 × (−5 − (−30)) = 2 × 25 = 50 dBc
Third-order IM product frequencies:
2f1 − f2 = 2 × 14.210 − 14.220 = 14.200 MHz ← RIGHT ON YOUR FREQUENCY
2f2 − f1 = 2 × 14.220 − 14.210 = 14.230 MHz
IM product power: −30 − 50 = −80 dBm
The noise floor of an HF receiver is typically around −130 dBm (in 2.4 kHz SSB bandwidth). A phantom signal at −80 dBm is 50 dB above the noise floor — a very strong, completely false signal sitting right on 14.200 MHz, the frequency you are trying to receive.
This scenario explains why serious DX and contest stations invest in high-IP3 receive preamplifiers, use extensive bandpass filtering before the first amplifying stage, or deliberately disable the preamplifier when signals are strong. Adding 10 dB of input attenuation improves IMD by 20 dB (the third-order products decrease 3 dB for every 1 dB reduction in input power). This is why the attenuator button on your transceiver is not just for reducing signal level — it directly improves the ratio of desired signal to IMD products.
Frequently Asked Questions
Why are third-order IM products more dangerous than second-order products in ham radio?
Second-order products fall at f1+f2 and f1−f2. When two signals are close together in frequency (as is normal within a single ham band), f1+f2 is far above both signals and easily filtered, while f1−f2 is very low (audio range) and also easily separated. Third-order products at 2f1−f2 and 2f2−f1 fall very close to f1 and f2 — within the receiver's IF passband — and cannot be filtered away. A narrowband IF filter designed to pass 2.4 kHz of SSB bandwidth cannot distinguish between a genuine signal at 14.200 MHz and an IM product at 14.200 MHz created from two signals 10 kHz and 20 kHz away.
Why does the 1 dB compression point matter for power amplifiers?
In a linear power amplifier used for SSB, the output must faithfully reproduce the complex envelope of the single-sideband signal. If the PA is driven into compression — above its P1dB — the gain decreases and the peaks are flattened, generating broadband IMD. This IMD splatter extends far beyond the intended SSB bandwidth of 2.4 kHz, potentially interfering with stations many kilohertz away. Most SSB PA design guidelines specify operating 6–10 dB below P1dB to keep IMD at acceptable levels. Driving an SSB amplifier harder than its rated PEP output to "get more output" causes severe IMD and interferes with other stations.
Does a higher gain preamplifier always improve receiver performance?
Not necessarily. A high-gain preamplifier improves sensitivity — the ability to hear weak signals — but reduces dynamic range because strong signals arrive at the next stage (the mixer or subsequent amplifier) at higher levels, more likely to cause IMD. The correct choice depends on the environment. On quiet bands from a rural site, a preamplifier improves the ability to hear very weak DX signals. On busy HF bands from an urban site during a contest, a preamplifier may create more IMD problems than it solves. Many modern transceivers include a switchable preamplifier and attenuator precisely so the operator can choose the right trade-off for current conditions.
How does Class of operation affect IMD in a power amplifier?
Class A amplifiers have the best linearity (lowest IMD) because the transistor operates in its linear region for the full 360° of the signal cycle and the Q-point is in the middle of the load line, far from saturation and cutoff. Class AB has good linearity when properly biased — the idle current eliminates crossover distortion and the transistors only approach saturation at peak signal. Class B has significantly worse IMD due to crossover distortion. Class C is highly non-linear and completely unsuitable for SSB or data modes; it is only used with narrowband tank circuits that filter harmonics and is used exclusively for CW or FM where constant carrier amplitude means constant collector current. IMD is not the relevant figure for Class C — harmonic suppression is.
Why does using the receiver's attenuator improve IMD even though it also reduces the desired signal?
IMD products grow faster than the desired signal as input power increases: third-order products increase 3 dB for every 1 dB increase in input power. Conversely, reducing input power by 1 dB reduces third-order IM products by 3 dB, while reducing the desired signal by only 1 dB. The net effect is a 2 dB improvement in signal-to-IMD ratio for each 1 dB of attenuation. A 10 dB attenuator improves the IMD situation by 20 dB while only reducing signal by 10 dB — often a worthwhile trade when strong nearby signals are causing phantom-signal problems.
Check Your Understanding
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