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harmonic of this half of the IF frequency plus the RF frequency mixing with the LO s second harmonic, with the resulting difference frequency falling dead in the receiver s IF band To mitigate this, any RF signals that are at half the IF plus the desired RF should be properly attenuated before they exit the first front-end receive filter These half-IF spurs in a receiver are fourth-order spurious or noise responses that are generated by the nonlinearities of the mixer and the frequency mixing of an interferer The RF frequencies that cause half-IF spurs are located in frequency midway between the receiver s LO and our wanted RF signal, producing a second-order spur that heterodynes with the second harmonic of the LO, creating an inband spur in the IF, and can be an issue both with high-side and low-side LO injection schemes When using low-side injection, any RF interferer at the receiver s front-end that is below the receiver s wanted frequency by fIF/2 [or fHALF IF = fr fIF/2 or fHALF IF = (fr + fLO)] For high-side injection, any RF interferer at the receiver s front-end that is above the wanted received frequency by fIF/2 (or fHALF IF = fr + fIF/2) can cause a spurious response in the IF passband For instance, if we had a low-side injection receiver that was tuned to 2 GHz (fr), and the receiver has an IF of 100 MHz (fIF), then we could expect that any signal at a frequency of fr fIF/2, 2 GHz 100 MHz/2 = 195 GHz, will cause a signal spur to be created directly on the receiver s 100-MHz IF frequency We can check this result by fIF = (2 fHALF IF) (2 fLO) Any mixer with a high IIP2 specification (greater than 45 dBm) will probably not generate a significant half-IF spur nor half-IF noise, since the spur is, as mentioned, caused by second-order distortions within the mixer.

expression in the next section) Summarizing, we can write the following transformations (sometimes called production rules):

Phase noise (Fig 94) is a noise similar to a modulated spectrum created by a virtual noise source that is phase modulating the desired signal All real-world receiver local oscillators are not perfect single continuous wave (CW) frequency sources, but possess noise sidebands, called phase noise Any receiver s modulation scheme that uses phase variations to communicate, especially dense modulations such as QAM-16 and above, are severely affected by the presence of this phase noise, since low phase noise is vital to maintain a receiver s SNR and BER (See Receiver Reciprocal Mixing ) Phase noise is measured as the ratio between the fundamental frequency and a noise sideband (in dBc), with the noise sideband located within a 1-Hz bandwidth at a

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All C programs begin with a call to main( ) and end when either the last } or a return has been encountered in main( ) assuming that exit( ) or abort( ) has not been called elsewhere Any other functions contained in the program must be either directly or indirectly called by main( ); thus, to execute a C program, simply begin at the start of the main( ) function and stop when main( ) ends This is precisely what Little C does C Expressions C expands the role of expressions relative to many other computer languages In general terms, a statement is either a C keyword statement, such as while or switch, or it is an expression For the sake of discussion, let's categorize all statements that begin with C keywords as keyword statements Any statement in C that is not a keyword statement is, by definition, an expression statement Therefore, in C the following statements are all expressions:

A mixer s local oscillator without phase noise (left), and with phase noise (right)

count = 100; /* line 1 */ sample = i / 22 * (c-10); /* line 2 */ printf(''This is an expression"); /* line 3 */

particular frequency that is offset from the LO s fundamental (in kHz) This phase noise specification may look like 95dBc/Hz@10kHz , which in this case means that the receiver s LO phase noise is measured at a 10-kHz offset from the LO s fundamental output frequency, and the noise power (in dBm) within a 1-Hz bandwidth is 95 dBc below the amplitude of the LO

Let's look more closely at each of these expression statements In C, the equal sign is an assignment operator C does not treat the assignment operation the way a language such as BASIC would, for example In BASIC, the value produced by the right side of the equal sign is assigned to the variable on the left But, and this is important, in BASIC, the entire statement does not have a value In C, the equal sign is an assignment operator, and the value produced by the assignment operation is equal to that produced by the right side of the expression Therefore, an assignment statement is actually an assignment expression in C; because it is an expression, it has a value This is why it is legal to write expressions such as the following:

34 35 36 36 36

We must decide on the optimal system specifications during the wireless receiver s planning phase, such as the most favorable IF/LO frequencies, mixer type/performance, filter topology/bandwidth, RF and IF amplifier IP3/NF/S21, and the best possible arrangement for all the required stages within the cascade This demands the use of a receiver or system simulation program or spreadsheet, such as RFcafe s RF Workbench, which is included on the enclosed CD, or RF Cascade Workbook, also by RFcafe

Page 721 a = b = c =: 100; printf(''%d", a=4+5);

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