Solution of ECE 342 Test 2 S12

Transcription

1 Soluion of ECE 342 Tes 2 S2. All quesions regarding superheerodyne receivers refer o his diagram. x c () Anenna B T < B RF < 2 f B = B T Oher Signals f c Mixer f Baseband x RFi RF () x RFo () () () x i x o Demodulaor x() Local Oscillaor f LO = f c ± f (a) A superheerodyne receiver is designed o receive signals wih carrier frequencies beween 4 and 6 MHz wih ransmied bandwidhs of 00 khz each. Is frequency is 850 khz. Wha range of local oscillaor frequencies is required using high-side injecion ( f LO > f c )? f LO = f c + f 4.85 MHz f LO 6.85 MHz (b) The RF amplifier/filer is an RLC parallel uned circui wih a -3 db bandwidh of 200 khz. I is uned o 5 MHz and he frequency is 850 khz wih high-side injecion. Wha is he numerical Q of he filer? Wha is he numerical image frequency f c? Wha is he image rejecion in db? Q = f o BW = = 25 The image frequency is f c = f c + 2 f = 6.7 MHz. H( f ) = + jq f f 0 f 0 f = f + j f H( f ) = + j = e j.5035 So he image rejecion is db. H( f ) db = 20log 0 ( ) = db

2 2. All quesions regarding phase-locked loops refer o hese diagrams, he mixer is an analog muliplier, x c sinusoidal and v ( ) is sinusoidal when he loop is locked. ( ) is x c () v() LPF VCO K a () + E( s) Φ( s) H( s) K Y( s) a y Φ v ( s) 2π / s (a) A phase-locked loop is locked wih an incoming signal frequency of MHz and a free-running VCO frequency of MHz and a VCO gain of 0 khz/vol and an amplifier gain of 5. Wha is he numerical phase shif beween x c ( ) and v ampliude and he loop is sill sable wha effec does ha have on he phase shif when he loop again reurns o a locked condiion? ( ) and which one is leading? If he inpu signal suddenly increases in v( ) leads x c ( ) by 90 There is no effec on he phase shif. I is sill 90. (b) A phase-locked loop is locked wih an incoming signal frequency of 00 khz and a free-running VCO frequency of 98 khz and a VCO gain of 0 khz/vol and an amplifier gain of 5. Assuming he LPF is ideal and compleely blocks he higher frequency from he mixer, wha is he numerical oupu volage y( ) in vols? Is he phase shif beween x c ( ) and v suddenly increases in ampliude and he loop is sill sable wha effec does ha have on he phase shif when he loop again reurns o a locked condiion? ( ) greaer han or less han 90? If he inpu signal y( ) = 0.2 V The phase shif is less han 90. Effec on phase shif is o move i closer o 90.

3 ( ) ( ) = sk a H( s) s + 2πK a H( s) where ( ) is he ransfer funcion of he lowpass filer. Le K a = 0 and = 0 khz/vol and le (c) The closed-loop ransfer funcion of a linearized phase-locked loop is Y s Φ s H s H( s) = 000. Find he numerical values of he poles for he overall sysem. Is he sysem sable? s ( ) ( ) = sk a H( s) 0s s + 2πK a H( s) = Y s Φ s 000 s = 000 s + 2π 0 5 s Poles are a s = 500 ± j2506. The sysem is sable. 0000s s s + 2π 0 8

4 3. Wha is he numerical frequency of he oupu signal from his frequency synhesizer (assuming he highpass filer is ideal and all signals are sinusoids)? HPF 230 MHz 200 PD VCO Corner Frequency = 230 MHz MHz The las mixer mixes 230 MHz wih 7 = 8.05 MHz. The wo mixer oupu frequencies are herefore MHz and MHz. Only he higher one ges hrough he highpass filer. So he oupu frequency is MHz.

5 4. Three signals are o be frequency-division muliplexed. All hree have baseband bandwidhs of 7 khz. Two subcarrier frequencies are used. One signal DSB modulaes he lower-frequency subcarrier, one of hem LSSB modulaes he higher-frequency subcarrier and one is unmodulaed (before he main modulaion which is AM). A guard band of 2 khz is required o avoid crossalk. Draw a skech of he specrum of he signals afer hey are added bu before he main modulaion. Indicae on he skech he numerical frequencies a he edges of he bands. The main carrier frequency is.2 MHz. The final AM modulaed signal lies beween wo frequency limis f low and f high in posiive frequency space. Wha are he numerical values of f low and f high? Baseband from -7 khz o 7 khz. Guard band from 7 khz o 9 khz. DSB modulaed signal from 9 khz o 23 khz. Guard band from 23 khz o 25 khz. LSSB modulaed signal from 25 khz o 32 khz. So he double-sided specrum sreches from -32 khz o 32 khz. When his AM modulaes a.2 MHz carrier, he bandpass signal ha resuls lies beween.68 MHz and.232 MHz.