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Taking the first case of high-side injection, the image is any signal or noise at the frequency that differs from the LO by the amount of the IF, just as the desired signal does, but is higher instead of lower than the local oscillator frequency Subtracting the desired signal from the local oscillator frequency will give the IF which will, of course, easily pass through the receiver s IF amplifiers But any frequency (the image) that is higher than the LO by the same amount that the signal is below the LO will also give us this same frequency This frequency will easily pass through all the IF amplifiers, and create receiver interference and a decrease in the signal-to-noise ratio (SNR) As mentioned, the dominant technique for attenuating this undesired image frequency is by front-end filtration The image filtering can be further assisted by using a high IF in order to remove the image as far away from the desired frequencies as possible This will make the filtering of the image a much easier task, and with a decreased risk of excessive group delay variations caused by an exceptionally tight filter Maintaining this first image far from the desired signal frequencies is assisted by utilizing double or even triple conversion receiver designs With these multiple conversion receivers, the first IF is at a high frequency, while the second and third IFs are progressively lower These lower IFs will supply most of the selectivity and gain, since the lower the frequency the cheaper, and the more stable, sensitive, and selective, the amplifiers will be This is due to the lower frequency circuit s decreased stray reactances, fewer feedback paths, and lower cost components If left unfiltered, the image would contribute up to 3 dB of excess noise So, the more we can reject the image frequency the more the image noise will decrease For instance, if we attenuated the image frequency at the mixer s input by 10 dB, then our receiver noise figure would only increase by 04 dB (instead of 3 dB) By attenuating the image frequency by 20 dB, the image noise will be removed almost completely, with a noise figure increase contribution of only 004 dB If we chose to not filter the image at all, and simply permitted the image noise to enter the receiver unattenuated and if we wanted to maintain the same level of system sensitivity as a fully image-filtered radio that would require that we compensated for the added 3 dB of excess noise We could do this by doubling the system transmitter s RF output power, which is very expensive in both price and DC current demands So, we can see why it is vital to filter the image band before it ever reaches the IF stages The first IF is not the only area of the receiver that has image frequency issues Any receiver with a second conversion stage may suffer from the effects of an image, in this case the second image Thus, sufficiently tight first IF filtering must be used in order to remove spurs that impact the second IF s image frequency band Therefore, first and second image rejection of at least 50 dB into the second IF is desired To clarify this further: the first image must be filtered at RF, as stated, but the receiver s second image frequency must be filtered within the first IF stages If this is not done, the first image will be spot-on the first IF s frequency band, while both the first and second images will be within the frequency band of the second IF And since the second image will always be within twice the frequency of the second IF (at 2 f2ND IF) of both the RF and the first IF frequencies, and the second IF is normally quite low in frequency, we can see that the filtering of the second image at RF is impossible, and that a tight first IF filtering scheme is the only option Indeed, due to the second image frequency s closeness to the first IF frequency, sometimes the only way to effectively attenuate the second image is to utilize a surface acoustic wave (SAW) filter This particular filter must be laid out on the printed circuit board (PCB) for maximum input-to-output port isolation, which is required to prevent.

for(a=0; a < 10; a=a+1) for(b=0; b < 10; b=b+1) for(c=0; c < 10; c=c+1) puts (''hi"); if( ) if( ) x = 10;

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the second image from simply blowing-by the SAW s high insertion loss and steep stopbands via the circuit board s many sneak RF paths When manipulating a spreadsheet (or formulas) to calculate the noise figure of a receiver, an important thing to keep in mind is that such a spreadsheet will not supply us with the receiver s worst-case noise figure, since it cannot take into account the image noise contribution (nor will it pay any attention to the consequences of bandwidth, voltage standing wave ratio (VSWR), and sneak noise paths) Thus, if the image noise is not attenuated, 3 dB must be added to any noise figure obtained via a spreadsheet calculation This added noise figure (NF) contribution is significant, and can literally destroy an otherwise perfect system design if not expected The removal of the image frequencies and the image noise is typically taken care of by two separate filters in many superheterodyne receivers, especially in higher end units These particular filters are called the image frequency reject (IFR) and the image noise reject (INR) filter An IFR filter will normally be placed just before the receiver s low-noise amplifier (LNA) However, it cannot remove the wideband LNA-generated noise that would still be injected directly into the mixer s port The mitigation of this particular noise source (as well as some of the image frequency) requires an INR filter, which is placed between the LNA and mixer stages (Fig 92)

Instead, you must write the code like this:

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for(a=0; a < 10; a=a+1) { for(b=0; b < 10; b=b+1) { for(c=0; c < 10; c=c+1) { puts("hi"); } } } if( ) { if( ) { x = 10;; } }

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