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 an audio amplifier, distortion makes music sound harsh and muddy. In a measurement system, it creates errors and false readings. In a receiver, it generates phantom signals on frequencies you are trying to receive, and in anything that transmits, it creates harmonics and spurious emissions that cause interference and break emission regulations.
There are two categories of distortion that every electronics designer 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 right among the wanted signals. Of these, IMD is often the more damaging, because the products can fall inside the band of interest where no filter can remove them.
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 — two notes in a chord, or two radio signals on neighboring channels — these products fall very close to f1 and f2, inside the 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 guitar amplifier deliberately driven into clipping might have 10% or more, which is the sound guitarists want. A speech amplifier for a public-address system might have 1–3% at full output — audible but acceptable for speech. A Class C RF power amplifier might have THD of 20% or more, but its tank circuit removes the harmonics before they reach the load.
Harmonics from anything that transmits are a regulatory concern. The ITU and national regulators set maximum harmonic and spurious emission levels, typically 40–60 dB or more below the wanted signal, for everything from broadcast transmitters to wireless modules and key fobs. The second and third harmonics of a 7 MHz signal fall at 14 MHz and 21 MHz — frequencies used by other services — so they must be suppressed before the signal leaves the equipment.
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 let strong AM broadcast stations (530–1,700 kHz) mix to produce false signals at their sum and difference frequencies, anywhere in its range.
The third-order products at 2f1−f2 and 2f2−f1 are the most damaging in narrowband systems. If f1 = 14.200 MHz and f2 = 14.210 MHz (two signals 10 kHz apart), the third-order products appear at 14.190 MHz and 14.220 MHz — right next to both signals, inside any reasonable filter passband. These spurious signals cannot be filtered away after the fact. The same thing happens in audio: two tones at 1,000 Hz and 1,100 Hz in a distorting amplifier produce products at 900 Hz and 1,200 Hz, unrelated to the music and therefore particularly unpleasant to hear.
The Two-Tone Test
The two-tone test is the standard measurement method for IMD in linear amplifiers. Two equal-amplitude sine wave tones are applied simultaneously to the amplifier input — for audio amplifiers often 19 kHz and 20 kHz (the CCIF test) or 60 Hz and 7 kHz (the SMPTE test), and for RF amplifiers two frequencies a few kilohertz apart. The output spectrum is examined on a spectrum analyzer (or with an FFT on an oscilloscope or sound card) to measure the amplitude of the IM products relative to the wanted 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. A good linear RF power amplifier achieves −30 to −40 dBc; a good audio amplifier, better than −80 dB (0.01%). An RF amplifier with only −20 dBc IMD produces “splatter” — distortion products that spread beyond the intended bandwidth and interfere with neighboring 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 small-signal amplifier. A MOSFET or cascode amplifier might achieve IIP3 = +10 to +20 dBm. A low-cost receiver chip or software-defined-radio front end might have IIP3 = −10 dBm, which explains why strong broadcast stations can create spurious signals in cheap 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 front end with IIP3 = 0 dBm, P1dB ≈ −10 dBm. Signals stronger than −10 dBm at the input will cause compression and significant IMD. That is a strong signal, but not an unusual one: a 100 W transmitter a few hundred meters away, or a mobile phone held next to a receiver, can easily deliver −10 dBm. This is why high-IP3 front ends matter in any receiver that must work near strong signals.
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 linear power amplifiers, Class AB is the standard for audio and for RF signals whose amplitude carries information, because it provides much lower distortion than Class B while maintaining better efficiency than Class A. Proper crossover bias is critical: too little idle current gives crossover distortion and poor IMD; too much idle current wastes power and causes the transistors to overheat.
Amplifier Class and Distortion
| Class | Conduction Angle | Typical IMD / THD | Distortion Type | Typical Use |
|---|---|---|---|---|
| A | 360° | Lowest — THD <1% at moderate output | Mainly 2nd harmonic (even-order) | Preamplifiers, small-signal amps, audio stages, oscillator buffers |
| AB | 180°–360° | Low — IMD typically −30 to −40 dBc | Crossover (if bias too low), else mainly 3rd order | Audio and linear RF 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 | Constant-amplitude RF stages with L/C tank output |
| D | Switching | Very low in-band after filtering | Switching transients; filtered by low-pass | Switching power supplies, some digital audio 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 Practice
The practical consequence of IMD in a receiver is desensitization and phantom signal generation. Here is how it plays out in a real-world scenario:
A receiver is tuned to 14.200 MHz. Two strong signals from nearby transmitters are on 14.210 MHz and 14.220 MHz, each arriving at about −30 dBm (a very strong signal). The receiver's front-end amplifier 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 (front-end amplifier)
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 THE TUNED FREQUENCY
2f2 − f1 = 2 × 14.220 − 14.210 = 14.230 MHz
IM product power: −30 − 50 = −80 dBm
The noise floor of a good receiver is around −130 dBm in a 2.4 kHz 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 the receiver is tuned to.
This scenario explains why high-performance receivers and spectrum analyzers use high-IP3 front-end amplifiers, extensive band-pass filtering before the first amplifying stage, and a switchable input attenuator. 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 setting on a spectrum analyzer is not just for reducing signal level — if a spurious signal drops by much more than the attenuation you add, it was being generated inside the analyzer, not present in the signal you are measuring.
Frequently Asked Questions
Why are third-order IM products more dangerous than second-order products?
Second-order products fall at f1+f2 and f1−f2. When two signals are close together in frequency, f1+f2 is far above both signals and easily filtered, while f1−f2 is very low (often in the audio range) and also easily separated. Third-order products at 2f1−f2 and 2f2−f1 fall very close to f1 and f2 — within the wanted passband — and cannot be filtered away. A filter designed to pass 2.4 kHz of 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 — audio or RF — the output must faithfully reproduce the shape of the input. If the amplifier is driven into compression (above its P1dB), the gain decreases and the peaks are flattened, generating a burst of harmonics and IMD. In an audio amplifier you hear this as harsh distortion on loud passages; in an RF amplifier it spreads the signal far beyond its intended bandwidth, interfering with neighboring channels. Most linear amplifier design guidelines specify operating several decibels below P1dB to keep distortion at acceptable levels. Driving an amplifier harder than its rated output to “get more power” produces only a little more power and a great deal more distortion.
Does a higher gain preamplifier always improve receiver performance?
Not necessarily. A high-gain preamplifier improves sensitivity — the ability to detect weak signals — but reduces dynamic range, because strong signals arrive at the next stage at higher levels, where they are more likely to cause IMD or clipping. The correct choice depends on the environment. Where all signals are weak, more gain helps. Where strong and weak signals are present together, too much gain early in the chain creates more distortion than it removes noise. This is why receivers, spectrum analyzers and audio interfaces offer switchable preamplifiers, attenuators or gain controls, so the user can choose the right trade-off for the signals present.
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 audio or for any signal whose amplitude carries information; it is used only with tuned tank circuits for constant-amplitude signals. IMD is not the relevant figure for Class C — harmonic suppression is.
Why does adding attenuation at a receiver or analyzer input improve IMD even though it also reduces the wanted 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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