EE242 Homework 1 Lingkai Kong February 9 2009 1 Solution In a Weaver receiver shown below the RF signal is RF mr cos LO1 IF1 t mi cos LO1 IF1 t We can calculate the signal at A B C D assuming the gain mismatch is and the phase mismatch is respectively 1 90 2 90 Figure 1 Weaver Architecture 1 EE242 Homework 1 Lingkai Kong ALP F 1 cos LO1 t RF 2 mi mr 1 cos IF1 t 1 cos IF1 t 2 2 2 2 BLP F 1 sin LO1 t RF 2 mr mi 1 sin IF1 t 1 sin IF1 t 2 2 2 2 CLP F 1 cos LO2 t ALP F 2 mi mr cos IF t 1 1 cos IF t 4 2 4 2 DLP F 1 cos LO2 t BLP F 2 mi mr cos IF t 1 1 cos IF t 4 2 4 2 1 Then we can combine the C and D signal at the output node as IF C D mr 1 1 cos IF t 1 1 cos IF t 4 2 2 mi 1 1 cos IF t 1 1 cos IF t 4 2 2 mr 1 cos cos IF t sin sin IF t 2 2 2 mi cos IF t 1 sin sin IF t cos 2 2 2 2 The image reject ratio is as following IR 10log 1 2 cos2 2 sin2 2 2 2 cos2 1 2 sin2 2 2 1 2 1 cos 2 1 cos 10log 2 1 cos 1 2 1 cos 2 3 Solution For a 1MHz communication system the wavelength is 300m which is 100X bigger than antenna size So we can take the antenna as a small antenna and 2 EE242 Homework 1 Lingkai Kong the radiation power factor can be calculated as 1 P Frad 1 kV 6 l3 4 where k is the shape factor and l 2 And the efficiency of the antenna can be written as P Frad 5 P Frad P Floss where P Floss is the loss power factor Now we assume the shape factor k 2 and then the radiation power factor is P Frad 1 2 3 2 92 10 6 3 6 c 2 f 6 Assuming the loss power factor is 0 0001 we can get the efficiency of the antenna is 2 92 10 2 15 3dB 7 So totally we will have 30dB loss from antenna Then we calculate the link budget according to following assumptions Type of parameters Data rate Symbol rate Noise figure Io No Required Eb No Antenna gain TX Antenna gain RX TX antenna hight RX antenna hight Carrier frequency Distance Transmission loss Reception loss Link margin value of parameters 10kHz 10kHz 10dB 3dB 30dB 1 76 dB 1 76dB 260m 2m 1MHz 100 miles 2dB 10dB 10dB Table 1 Assumptions for link budget calculation According to these assupmtions we can calculate the required output power should be 26dBm Plug in the efficiency of the antenna the total output 3 EE242 Homework 1 Lingkai Kong power at the output of PA will be 56dBm which is about 400W Comparing AM with FM since FM requires more bandwidth the noise power in FM system is higher than AM which leads to more power consumption 3 Solution Because it is not matched after the signal is down convertered we express the gain and NF of the mixer IF filter and VGA in term of voltage instead of power The noise figure of mixer IF filter VGA is N F3 4 5 N F3 v2 N F4 1 N F5 1 n 1 2 G3 G3 G4 vn0 8 Given the input impedance of the mixer is 300 the input referred noise power should be Pn3 4 5 2 N F3 4 5 1 vn0 N F3 4 5 1 Pn0 R0 R300 R300 9 So the noise figure of mixer IF filter VGA in term of power should be N F3 4 5 1 R0 1 R300 10 So the noise figure of the entire front end should be N F N F1 N F2 1 R0 N F4 1 N F5 1 N F3 1 11 G1 G1 G2 R300 G3 G3 G4 Here G1 G2 N F1 N F2 are expressed in power and G3 G4 G5 N F3 N F4 N F5 are in term of voltage The voltage gain of the system is G R300 G1 G 2 G 3 G 4 G 5 R0 The IIP3 can be calculated as G1 R300 G1 G2 G1 G2 G3 G1 G2 G3 G4 1 1 IIP 3 IIP 31 IIP 32 R0 IIP 33 IIP 34 IIP 35 12 13 If we specify the Gain NF and IIP3 for each block as table2 we can get the overall performance as table3 which meets the requirement 4 EE242 Homework 1 Block RF Filter LNA mixer IF filter VGA Lingkai Kong Gain NF IIP3 1dB 1dB 100dBm 15dB 1 5dB 0dBm 10dB 8dB 16dBm 5dB 5dB 100dBm referred to 50 65dB 15dB 20dBm referred to 50 Table 2 Spec for each block Voltage Gain 91 78dB NF 2 74dB IIP3 9 71dBm Table 3 Overall performance 5