4/12/2005 Image and Third Order Product Rejection.doc 1/9 Jim Stiles The Univ. of Kansas Dept. of EECS Image and Third-Order Signal Rejection Recall in a previous handout the example where a receiver had an IF frequency of 30IFfMHz= . We desired to demodulate a radio station operating at 100 MHz, so we set the LO to a frequency of 130LOfMHz= (i.e., high-side tuning). We discovered that RF signals at many other frequencies would likewise produce signals at precisely the IF frequency of 30 MHz—a very serious problem that can only be solved by the addition of a preselector filter. Recall that this preselector filter must allow the desired signal (or band of signals) to pass through unattenuated, but likewise must sufficiently reject (i.e., attenuate) all the RF signals that could create spurious signals at the IF frequency. We found for this example that these RF signals reside at frequencies: 10 MHz, 15 MHz, 30 MHz, 80 MHz, 160 MHz, 230 MHz, and 290 MHz Note that the most problematic of these RF signals are the two at 80 MHz and 160 MHz.4/12/2005 Image and Third Order Product Rejection.doc 2/9 Jim Stiles The Univ. of Kansas Dept. of EECS Q: Why do these two signals pose the greatest problems? A: Because the frequencies 80 MHz and 160 MHz are the closest to the desired signal frequency of 100 MHz. Thus, they must be the closest to the pass-band of the preselector filter, and so will be attenuated the least of all the RF signals in the list above. As a result, the 30 MHz mixer products produced by the RF signals at 80 MHz and 160 MHz will be likely be larger than those produced by the other problem frequencies—they are the ones most need to worry about! Let’s look closer at each of these two signals. Image Frequency Rejection We determined in an earlier handout that the radio frequency signal at 160 MHz was the image frequency for this particular example. Recall the image frequency is the other RFf solution to the (ideal) second-order mixer term RF LO IFff f−=! For low-side tuning, the desired RF signal is (by definition) the solution that is greater than LOf: RF LO IFfff=+ (low-side tuning)4/12/2005 Image and Third Order Product Rejection.doc 3/9 Jim Stiles The Univ. of Kansas Dept. of EECS And thus the image signal is the solution that is less than LOf: image LO IFfff=− (low-side tuning) Similarly, for high-side tuning, the desired RF signal is (by definition) the solution that is less than LOf: RF LO IFfff=− (high-side tuning) And thus the image signal is the solution that is greater than LOf: image LO IFfff=+ (high-side tuning) Note for both high-side and low-side tuning, the difference between the desired RF signal and its image frequency is 2IFf: 2RF image IFff f−= This is a very important result, as is says that we can increase the “distance” between a desired RF signal and its image frequency by simply increasing the IF frequency of our receiver design!4/12/2005 Image and Third Order Product Rejection.doc 4/9 Jim Stiles The Univ. of Kansas Dept. of EECS For example, again consider the FM band (88 MHz to 108 MHz). Say we decide to design an FM radio with an IF of 2O MHz, using high-side tuning. Thus, the LO bandwidth must extend from: 88 10888 20 108 20108 128IF LO IFLOLOff fff+<< ++< < +<< The image bandwidth is therefore: 108 128108 20 128 20128 148IF image IFimageimageff fff+< < ++< < +<< Thus, the preselector filter for this FM radio must have pass-band that extends from 88 to 108 MHz, but must also sufficiently attenuate the image signal band extending from 128 to 148 MHz. Note that 128 MHz is very close to 108 MHz, so that attenuating the signal may be very difficult. Q: By how much do we need to attenuate these image signals?4/12/2005 Image and Third Order Product Rejection.doc 5/9 Jim Stiles The Univ. of Kansas Dept. of EECS A: A very good question; one that leads to a very important point. Since the image frequency creates the same second-order product as the desired signal, the conversion loss associated with each signal is precisely the same (e.g. 6 dB)! As a result, the IF signal created by image signals will typically be just as large as those created by the desired FM station. This means that we must greatly attenuate the image band, typically by 40 dB or more! Q: Yikes! It sounds like we might require a filter of very high order!?! A: That’s certainly a possibility. However, we can always reduce this required preselector filter order if we simply increase our IF design frequency! To see how this works, consider what happens if we increase the receiver IF frequency to 40IFfMHz=. For this new IF, the LO bandwidth must increase to: 88 10888 40 108 40128 148IF LO IFLOLOff fff+<< ++<< +<< The new image bandwidth has therefore increased to:4/12/2005 Image and Third Order Product Rejection.doc 6/9 Jim Stiles The Univ. of Kansas Dept. of EECS 108 128128 40 148 40168 188IF image IFimageimageff fff+< < ++< < +<< Note this image band is now much higher in frequency than the FM band—and thus much more easily filtered! The amount by which the preselector attenuates the image signals is known as the image rejection of the receiver. For example, if the preselector filter attenuates the image band by at least 50 dB, we say that the receiver has 50 dB of image rejection. 88 108 128 148 168 188 f (MHz) FM band Image band for fIF=20 Image band for fIF=40 ()fTfIF=20 image rejection fIF=40 image rejection4/12/2005 Image and Third Order Product Rejection.doc 7/9 Jim Stiles The Univ. of Kansas Dept. of EECS So by increasing the IF frequency, we can either get greater image rejection from the same preselector filter order, or we can reduce the preselector filter order while maintaining sufficient image rejection. But be careful! Increasing the IF frequency will also tend to increase cost and reduce detector performance. 3rd-Order Signal Rejection In addition to the image frequency (the other solution to the second order term RF LO IFff f−=), the other radio signals that are particularly difficult to reject are the fRF solutions to the 3rd order product terms 2RF LO IFff f−= and 2LO RF IFff f−=. There are four possible RF solutions (two for each term): 12LO IFfff+= Å 22LO IFfff−= 32LO IFfff=+ 42LO IFfff=− Å4/12/2005 Image and Third Order Product Rejection.doc 8/9 Jim Stiles The Univ. of Kansas