Overview
Nonlinearity in amplifiers is a common phenomenon in semiconductor devices, and it becomes more pronounced when the input signal amplitude is large. Because amplifiers provide gain, they are more susceptible to nonlinear distortion than many other semiconductor components. This article uses amplifiers as an example to discuss intermodulation distortion (IMD) and test methods.
Impact of intermodulation distortion on systems
Intermodulation distortion affects both the transmit and receive chains of wireless communication systems.
In the transmit chain, the power amplifier is the component most vulnerable to nonlinear effects. For wideband modulated signals, significant intermodulation components are generated both inside and outside the signal band. Out-of-band intermodulation components cause interference to other channels and are typically measured by adjacent channel leakage ratio (ACLR) or adjacent channel power ratio (ACPR). In-band intermodulation components interfere with the desired signal, reducing signal-to-noise or signal-to-distortion ratios. For satellite communication systems, the noise power ratio (NPR) is an important metric.
In the receive chain, the main concern is intermodulation distortion in the front-end low-noise amplifier (LNA). When strong two-tone or multi-tone interferers exist near the signal, IMD products can fall into the signal bandwidth and degrade receiver sensitivity. The mobile phone two-tone sensitivity test addresses this scenario by applying two-tone interferers on adjacent channels to evaluate receiver sensitivity under those conditions. Standards define the frequencies and amplitudes of the two-tone interferers and require the receiver to meet specified sensitivity limits. Therefore, RF front-end LNAs require good linearity.
In summary, IMD has significant effects on transmit and receive performance in wireless systems. Nonlinear performance is an important consideration in RF amplifier design and tuning.
Mechanism of intermodulation distortion
When a single-tone input is applied to an amplifier, the output contains the fundamental frequency and its harmonics. With two-tone or multi-tone inputs, amplifier nonlinearity produces combinations of the input frequencies, generating intermodulation products.
From a spectral perspective, the closest IMD products to the fundamental tones are the third-order difference products, at frequencies 2ω1 ? ω2 and 2ω2 ? ω1. In wideband systems these components cause the most significant interference to the desired signal and adjacent channels. Third-order IMD products also tend to have relatively large amplitudes compared with higher-order products, which is why vendor-specified IMD parameters usually refer to third-order distortion.
Intermodulation is not limited to the third-order terms of a Taylor series expansion; fifth-, seventh-, and higher odd-order terms also appear, but their contributions diminish as order increases.
Coefficients for fundamental and third-order IMD (up to 5th order)
For quantitative analysis, Table 1 lists the coefficients for the fundamental and third-order intermodulation terms resulting from a Taylor series expansion up to the fifth-order term.
Table 1. Coefficients of fundamental and 3rd-order intermodulation (up to 5th order)
| coefficient | cos(2ω1?ω2)t | cos(ω1 t) | cos(ω2 t) | cos(2ω2?ω1)t |
|---|---|---|---|---|
| (cos ω1 t + cos ω2 t)^1 | 0 | 1 | 1 | 0 |
| (cos ω1 t + cos ω2 t)^2 | 0 | 0 | 0 | 0 |
| (cos ω1 t + cos ω2 t)^3 | 3/4 | 9/4 | 9/4 | 3/4 |
| (cos ω1 t + cos ω2 t)^4 | 0 | 0 | 0 | 0 |
| (cos ω1 t + cos ω2 t)^5 | 25/8 | 25/4 | 25/4 | 25/8 |
Behavior in logarithmic coordinates
From a log-power perspective, the following conclusions apply:
- The output power of both the fundamental and third-order IMD products does not change linearly with input power across the full dynamic range.
- At low input power, the output powers of the fundamental and third-order IMD are approximately linear with input power. This approximate linearity is important when calculating the third-order intercept point (IP3).
- In the approximate linear region, the third-order IMD power increases three times faster with input power than the fundamental power does.
- At sufficiently low input power (typically well below 0 dBm), third-order IMD components are much lower in power than the fundamental.
- As input power increases further, nonlinear compression becomes apparent for both the fundamental and third-order IMD output power curves.
Third-order IMD is commonly characterized by two parameters: IMD3 (3rd order intermodulation distortion) and IP3 (3rd order intercept point). IP3 refers to the input or output power level at which the extrapolated linear responses of the fundamental and third-order IMD would intersect. In practice, the actual device rarely operates at the IP3 power level; IP3 is used as a standardized figure of merit for device nonlinearity.
Within the approximate linear region, a 1 dB increase in input power typically worsens IMD3 by 2 dB; conversely, a 1 dB reduction in input power improves IMD3 by 2 dB. This relationship does not hold once the device leaves the approximate linear region.
How to measure IMD3 and IP3
Measuring IMD3 and IP3 is straightforward but requires attention to detail to ensure accurate results.
Testing third-order intermodulation requires applying equal-amplitude two-tone signals and setting the tone spacing according to the device under test. For IMD3 measurements the tone amplitudes can be large or small, but when measuring IP3 the amplitudes must be low enough to ensure the device operates in the approximate linear region.
Commonly used approaches include using two signal generators to provide the two tones, which yields relatively pure two-tone signals. Alternatively, a vector signal generator can output a two-tone baseband waveform on a single channel by editing the baseband file, but this method can introduce some inherent third-order distortion in the generated signal and is usually used only when two generators are unavailable.
Pay special attention to the spectrum analyzer settings to avoid driving the analyzer itself into a nonlinear region, which would generate its own third-order products and corrupt the measurement. The spectrum analyzer will produce some IMD, but it must be small compared with the DUT IMD to avoid influencing the result.
Practical guidance:
- When measuring IMD3, increase the spectrum analyzer's input attenuation to evaluate whether the analyzer contributes significant IMD. If the measured third-order product does not change appreciably with increased attenuation, the analyzer's IMD contribution can be neglected. If the third-order product decreases as attenuation increases, continue increasing attenuation until changes are negligible. Note that using attenuation reduces measurement dynamic range; in those cases a notch filter to attenuate the fundamentals can be used to prevent the analyzer from generating strong IMD.
- When testing power amplifiers, always use an attenuator with adequate power rating before the spectrum analyzer to prevent damage. To achieve a higher dynamic range, use a notch filter to attenuate the fundamental tones.
Regarding the signal sources, two issues deserve attention. First is the two-tone amplitude. For IMD3 measurements the amplitude requirement is not strict, but for IP3 measurements the input amplitude must be kept low enough that the amplifier remains in the approximate linear region. A practical recommendation is to keep the two-tone amplitude at least 20 dB below the amplifier input power corresponding to the 1 dB compression point (Pin, 1 dB).
When recording IMD3 or IP3 results, always document the tone spacing and the two-tone amplitude. A useful verification method is: if increasing the input power by 1 dB worsens IMD3 by 2 dB, the amplifier is still in the approximate linear region and IP3 can be calculated.
Another issue is that the combiner output in the test setup may already contain third-order products, which can result from the signal generator's automatic level control (ALC) loop interacting with limited port isolation of the combiner. Reflected signals can re-enter the signal generators and, through the ALC loop, cause the generators to output two-tone and intermodulation components.
Before testing, use a spectrum analyzer to inspect the two-tone signal for any significant third-order distortion.
Reducing test artifacts
Most signal generators allow manual disabling of automatic level control (ALC), which prevents the described ALC-induced intermodulation but may reduce output power stability.
Other mitigation strategies include replacing the combiner with a high-isolation coupler or placing attenuators at each signal generator output to increase isolation between sources.
