### INTERMODULATION PRODUCTS OF TWO DIFFERENT FREQUENCIES

FREQUENCIES INTERMODULATION INFORMATION

Understanding the dynamic performance of the receiver requires knowledge of intermodulation products (IP) and how they affect receiver operation. Whenever two signals at frequencies F1 and F2 are mixed together in a non-linear circuit, a number of products are created according to the mF1 ± nF2 rule, where m and n are either integers or zero (0, 1, 2, 3, 4, 5, . . .).

Mixing can occur in either the mixer stage of a receiver front end, or in the RF amplifier (or any outboard preamplifiers used ahead of the receiver) if the RF amplifier is overdriven by a strong signal. It is also possible for corrosion on antenna connections, or even rusted antenna screw terminals to create IPs under certain circumstances.

One even hears of alleged cases where a rusty downspout on a house rain gutter caused re-radiated intermodulation signals. The order of an IP product is given by the sum (m + n). Given input signal frequencies of F1 and F2, the main IPs are:

Second order: F1 ± F2 2F1 2F2
Third order: 2F1 ± F2 2F2 ± F1 3F1 3F2
Fifth order: 3F1 ± 2F2 3F2 ± 2F1 5F1 5F2

When an amplifier or receiver is overdriven, the second-order content of the output signal increases as the square of the input signal level, while the third-order responses increase as the cube of the input signal level.

Consider the case where two HF signals, F1 = 10 MHz and F2 = 15 MHz are mixed together. The second order IPs are 5 and 25 MHz; the third-order IPs are 5, 20, 35 and 40 MHz; and the fifth-order IPs are 0, 25, 60 and 65 MHz.

If any of these are inside the passband of the receiver, then they can cause problems. One such problem is the emergence of ‘phantom’ signals at the IP frequencies. This effect is seen often when two strong signals (F1 and F2) exist and can affect the front-end of the receiver, and one of the IPs falls close to a desired signal frequency, Fd.

If the receiver were tuned to 5 MHz, for example, a spurious signal would be found from the F1–F2 pair given above. Another example is seen from strong in-band, adjacent channel signals. Consider a case where the receiver is tuned to a station at 9610 kHz, and there are also very strong signals at 9600 kHz and 9605 kHz. The near (in-band) IP products are:

Third-order: 9595 kHz ( F = 15 kHz)
9610 kHz ( F = 0 kHz) (ON CHANNEL!)
Fifth-order: 9590 kHz ( F = 20 kHz)
9615 kHz ( F = 5 kHz)

Note that one third-order product is on the same frequency as the desired signal, and could easily cause interference if the amplitude is sufficiently high. Other third- and fifth order products may be within the range where interference could occur, especially on receivers with wide bandwidths.

The IP orders are theoretically infinite because there are no bounds on either m or n. However, because the higher order IPs have smaller amplitudes only the second-order, third-order and fifth-order products usually assume any importance.

Indeed, only the third-order is normally used in receiver specification sheets because they fall close to the RF signal frequency.

There are a large number of IMD products from just two signals applied to a non-linear medium. But consider the fact that the two-tone case used for textbook discussions is rarely encountered in actuality. A typical two-way radio installation is in a signal rich environment, so when dozens of signals are present the number of possible combinations climbs to an unmanageable extent.