How do I calculate the level of second and third order intermodulation products?
Intermodulation Product Calculation
Intermodulation products arise from the nonlinear transfer function of active devices. Any nonlinearity can be expressed as a power series: Vout = a1·Vin + a2·Vin² + a3·Vin³ + ..., where the higher-order coefficients (a2, a3) represent the nonlinearity. When two tones at frequencies f1 and f2 are applied, the squaring term (a2) produces products at f1±f2, 2f1, and 2f2. The cubing term (a3) produces products at 2f1±f2, 2f2±f1, 3f1, and 3f2.
| Parameter | Class A | Class AB | Class F/Doherty |
|---|---|---|---|
| Max Efficiency | 50% | 50-78% | 70-90% |
| Linearity | Excellent | Good | Moderate (needs DPD) |
| P1dB Backoff | 0-3 dB | 3-6 dB | 6-10 dB |
| Complexity | Low | Low | High |
| Common Use | Test, small signal | General PA | Base station, broadcast |
Frequently Asked Questions
What about higher-order products?
Fifth-order products (3f1-2f2) grow at 5 dB/dB and are at 4×(Pin-OIP5) dBc. Seventh-order products grow at 7 dB/dB. Higher orders are usually negligible except in highly nonlinear systems or when many carriers are present, creating a dense spectral forest of products.
Are IM2 or IM3 more important?
IM3 dominates in narrowband systems because the products fall in-band. IM2 dominates in wideband or direct-conversion receivers where the f1-f2 product can fall at baseband. Direct-conversion receivers require very high IIP2 (typically +50 to +70 dBm) to prevent IM2 from corrupting the desired signal.
How many IM products exist with N tones?
With N tones, the number of third-order IM products grows as N²(N-1)/2. For 2 tones: 2 products. For 10 tones: 450 products. For 100 tones: 495,000 products. This is why multi-carrier systems like OFDM are extremely sensitive to IM distortion.