Intermodulation Distortion

When two or more signals at frequencies f1 and f2 pass through a nonlinear power amplifier, IMD generates new spectral components at sum and difference frequencies:

• Third-order products: 2f1 - f2 and 2f2 - f1 (most problematic, fall in-band)
• Fifth-order products: 3f1 - 2f2 and 3f2 - 2f1
• Second-order products: f1 + f2 and f1 - f2 (often out-of-band) The third-order products are particularly dangerous because they appear within the original signal bandwidth and cannot be filtered.

The IP3 is a theoretical figure of merit that quantifies a power amplifier's linearity. It represents the extrapolated output power level where the fundamental tone and third-order IMD product amplitudes would intersect:

• A higher IP3 indicates better linearity and lower IMD
• Typically specified as Output IP3 (OIP3) or Input IP3 (IIP3)
• The slope of the fundamental is 1:1 while the third-order IMD slope is 3:1 on a log-log power plot
• Every 1 dB increase in input power produces a 3 dB increase in third-order IMD power

IMD causes spectral regrowth, where the transmitted signal's spectrum broadens beyond its allocated channel bandwidth. This is quantified by the Adjacent Channel Leakage Ratio (ACLR):

• ACLR measures the ratio of power in the main channel to power leaking into adjacent channels
• Typical 3GPP requirements demand ACLR better than -45 dBc for base stations
• Spectral regrowth is the primary reason IMD must be suppressed through digital pre-distortion
• The regrowth bandwidth for third-order IMD is three times the original signal bandwidth

IMD behavior differs significantly between test tones and real communication signals:

• Two-tone testing provides clean, discrete IMD products ideal for characterization
• Modulated signals (OFDM, QAM) produce noise-like IMD that spreads continuously across the spectrum
• The peak-to-average power ratio (PAPR) of modern signals causes the amplifier to operate across a wide range of instantaneous power levels
• Real-world IMD prediction requires Volterra series models with memory to capture the dynamic nonlinear behavior under modulated excitation

In wideband power amplifiers, IMD is not purely instantaneous. Memory effects cause the distortion to depend on past signal values:

• Electrical memory: Bias network impedance variations at envelope frequencies modulate the IMD phase
• Thermal memory: Self-heating of the transistor channel changes gain and phase response over microsecond timescales
• Trapping effects: Charge trapping in GaN HEMT devices creates long-time-constant memory spanning milliseconds
• Memory effects cause asymmetry in IMD sidebands, where the upper and lower IMD products have unequal amplitudes

Doherty power amplifiers exhibit complex IMD behavior due to their load modulation architecture:

• The carrier amplifier operates in Class-AB while the peaking amplifier operates in Class-C
• IMD cancellation occurs at specific power levels where the two paths combine optimally
• The AM-PM distortion in Doherty amplifiers is particularly severe and varies with power level
• Digital pre-distortion for Doherty amplifiers requires generalized memory polynomial models to capture the unique nonlinear dynamics of the load modulation process

A figure of merit for quantifying third-order nonlinearity. IP3 is the theoretical point where the extrapolated fundamental tone power equals the extrapolated third-order intermodulation product power.

• Input IP3 (IIP3): Referenced to the input power
• Output IP3 (OIP3): Referenced to the output power
• Higher IP3 values indicate better linearity
• Typically 10-15 dB above the 1 dB compression point

Used extensively in cascaded system analysis to predict overall receiver or transmitter linearity.

The primary regulatory metric for quantifying spectral regrowth caused by IMD. ACLR measures the ratio of transmitted power within the assigned channel to the power leaking into adjacent channels.

• Defined by 3GPP for LTE and 5G NR compliance
• Typical requirement: -45 dBc or better for base stations
• Directly impacted by odd-order IMD products
• Wideband signals cause IMD to spread across multiple adjacent channels

Failure to meet ACLR limits results in regulatory non-compliance and network interference.

The classic experimental method for characterizing IMD. Two closely spaced sinusoidal tones at frequencies f1 and f2 are applied to the device under test.

• Third-order products appear at 2f1 - f2 and 2f2 - f1
• Fifth-order products appear at 3f1 - 2f2 and 3f2 - 2f1
• Tone spacing is typically 1 MHz or less for PA characterization
• Simplifies analysis compared to modulated signals

While not representative of real communication signals, the two-tone test provides a standardized, repeatable linearity benchmark.

The two fundamental nonlinear mechanisms that generate IMD. AM-AM distortion is the nonlinear relationship between input amplitude and output amplitude, causing gain compression. AM-PM distortion is the amplitude-dependent phase shift.

• AM-AM produces symmetric spectral regrowth
• AM-PM produces asymmetric spectral regrowth
• Memory effects cause frequency-dependent asymmetry
• Both must be corrected simultaneously by digital predistortion

Modern DPD systems model both effects using complex baseband Volterra series to achieve full linearization.

A signal conditioning technique applied before the power amplifier to reduce the peak-to-average power ratio (PAPR), thereby minimizing the generation of IMD products.

• Clipping and filtering reduces peak excursions
• Peak windowing applies smooth attenuation around peaks
• Reduces the PA's operating point swing into deep compression
• Works synergistically with DPD for optimal linearity

CFR is essential in modern OFDM systems where high PAPR signals would otherwise drive the PA into highly nonlinear regions, generating severe IMD.

A comprehensive in-band signal quality metric that captures the aggregate effect of IMD and other impairments on the modulated signal constellation.

• Measures the deviation of actual symbols from ideal reference points
• Expressed as a percentage or in dB relative to the signal power
• 5G NR 256-QAM requires EVM below 3.5%
• IMD products falling within the signal bandwidth directly degrade EVM

While ACLR measures out-of-band emissions, EVM quantifies the in-band distortion that reduces data throughput and increases bit error rate.