Static Non-Linearity

The defining characteristic of static non-linearity is that the output depends only on the instantaneous input amplitude, not on past signal history. This is typically modeled as a polynomial series:

• Vout = a0 + a1*Vin + a2*Vin² + a3*Vin³ + ...
• Coefficients a2, a3, etc. quantify the non-linear behavior
• No frequency-dependent terms or time constants are involved

This contrasts with dynamic non-linearity, where effects like slew-rate limiting and memory effects introduce history-dependent distortion.

When a single sinusoidal tone passes through a static non-linear system, it generates integer multiples of the fundamental frequency:

• Second harmonic (2f): Caused by quadratic (a2) term
• Third harmonic (3f): Caused by cubic (a3) term
• Even-order harmonics from asymmetric transfer curves
• Odd-order harmonics from symmetric (odd-function) non-linearities

The relative amplitudes of these harmonics form a unique spectral signature tied to the specific polynomial coefficients of the device.

When two or more tones are applied simultaneously, static non-linearity produces sum and difference frequency products:

• Second-order IMD: f1 ± f2
• Third-order IMD: 2f1 ± f2 and 2f2 ± f1
• These products fall near the original signals, making them difficult to filter
• The Third-Order Intercept Point (IP3) quantifies this behavior

IMD products reveal the exact polynomial transfer function and are a rich source of device-specific fingerprint features.

Static non-linearity manifests as two measurable conversion phenomena:

• AM-AM Conversion: Amplitude modulation of the input causes a non-linear change in output amplitude. Plotted as output power vs. input power, the curve deviates from the ideal 1:1 slope at saturation.
• AM-PM Conversion: Amplitude variations at the input cause unintended phase shifts at the output. This is critical because phase modulation is added to signals that should be pure amplitude-modulated.

Both curves are highly repeatable per device and serve as robust fingerprint dimensions.

In digitally modulated signals with non-constant envelopes, static non-linearity causes spectral regrowth—the expansion of the signal's bandwidth into adjacent channels:

• The polynomial non-linearity effectively convolves the signal spectrum with itself
• Third-order non-linearity spreads the spectrum by a factor of 3
• The Adjacent Channel Power Ratio (ACPR) quantifies this leakage
• The specific shape of the regrown spectrum is a direct function of the device's polynomial coefficients

This is a primary metric for power amplifier linearity and a distinctive fingerprint feature.

At high input amplitudes, the effective gain of a non-linear device decreases from its small-signal value:

• 1 dB Compression Point (P1dB): The input power at which gain drops by 1 dB from ideal
• Beyond P1dB, the device enters saturation, producing severe harmonic and IMD products
• The exact shape of the compression knee is process-dependent and varies per device
• This non-linear saturation behavior creates a distinct, high-power fingerprint region

Gain compression is a universal characteristic of all active RF components.

The maximum deviation of a converter's actual transfer function from an ideal straight line, measured after correcting for gain and offset errors. INL is a process-dependent signature that accumulates across the entire input range, creating a unique, low-frequency distortion pattern. It is typically expressed in units of Least Significant Bits (LSBs) and directly shapes the polynomial coefficients used to model a device's static non-linearity.

The deviation between an actual analog step width and the ideal 1 LSB step. DNL is a code-by-code imperfection that reveals localized irregularities in the converter's transfer function. Key characteristics include:

• Missing Codes: Occur when DNL < -1 LSB, creating a permanent, highly distinctive gap in the output.
• Wide Codes: Occur when DNL > 0, stretching a specific digital code's input range. These granular errors form a high-resolution, device-specific fingerprint.

The ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency. THD is the direct spectral manifestation of static non-linearity, where a polynomial transfer function generates energy at integer multiples of the input signal. The specific amplitude and phase of each harmonic (2nd, 3rd, etc.) are determined by the polynomial coefficients, making THD a quantifiable, frequency-domain fingerprint.

Non-linear products generated when two or more signals at different frequencies (f1, f2) are applied to a non-linear system. Static non-linearity creates new frequency components at sums and differences of the originals (e.g., 2f1-f2, 2f2-f1). The power and phase of these third-order intermodulation products are highly sensitive to the exact polynomial transfer function, providing a multi-tone signature that is richer than single-tone harmonic analysis.

A theoretical figure of merit that extrapolates the power level at which third-order intermodulation products would equal the fundamental tones. IP3 is a concise, single-number descriptor of a device's third-order non-linearity. While it is a simplified model, the Input IP3 (IIP3) and Output IP3 (OIP3) values are consistent for a given device and can serve as a coarse, high-level feature for fingerprinting and device classification.

The two fundamental static linear imperfections that form the baseline of a device's analog fingerprint:

• Gain Error: The deviation of the transfer function's slope from the ideal, scaling the entire output.
• Offset Error: A constant DC voltage shift between the ideal and actual transfer function. Though simple, these errors are highly stable over time and temperature, providing a persistent, easily extractable bias that distinguishes one device from another before any non-linear analysis is performed.