Components Required: Small bread-board to build the circuit on( or just use clip leads directly) 2ea 220pF capacitors 1 ea 1nF 10uH inductor

Transcription

1 EELE445 Lab 3: Whit nois, ½H(f)½, and a x3 Frquncy Multiplir Purpos Th purpos of th lab is to bcom acquaintd with PSD, whit nois and filtrs in th tim domain and th frquncy domain. Whit nois and swpt sin wavs ar usd xamin th to show th transfr function ½H(f)½ of a LPF (lowpass filtr), and a BPF (bandpass filtr). Th Q of th BPF is considrd. Th nois out of th BPF is considrd. Th a squar wav is compard going into th BPF and out of th filtr. Th filtr output is a sin wav at thr tims th frquncy of th squar wav. Th amplituds of undsird signals ar masurd. Componnts Rquird: Small brad-board to build th circuit on( or just us clip lads dirctly) a 0pF capacitors 1 a 1nF 10uH inductor Pr-lab Find th frquncis for a RC lowpass filtr with R=50 ohm and C-0pF whr th magnitud rspons is -3dB, -6dB, -10dB, -0dB, -40dB. Calculat th cntr frquncy, Q and 3 db bandwidth across a paralll RLC with R=5, C=1.9nF, and L=0nH. What is th quivalnt nois bandwidth, B n of th filtr for your calculation? (B n =B 3dB * p/) f 0 R 1 Rmmbr for a Bandpass filtr: Q = = X L = w 0L w0 = and B is th - B X L RC 3dB bandwidth. Singl pol Buttrworth Bandpass frquncy Rspons: ( ) 1 Hf () æ 1 + Q ç f f o è + f o f ö ø B abl to calculat th distortion of a sinwav with harmonics. (nots attachd) 1 of 13

2 METHOD: EELE445 Lab 3: Whit nois, ½H(f)½, and a x3 Frquncy Multiplir Gnrator Nois in Tim and Frquncy Domains 1) St th gnrator for a nois (random) signal output with Vp-p into a 50 ohm load. Vrify your amplitud stting using a sin wav. St th oscilloscop for sampl rat of 50Ms/sc, input R=50, and th bandwidth to 150 MHz. a) Masur th p-p, rms, and DC magnitud of th nois wavform using th oscilloscop. B sur th nois is not clipping. Hint(us th run stop button) Why is it not rading vp-p? Calculat th Vp-p to Vrms ratio. What do w us this ratio for? b) Using th Spctrum Analyzr (SA) to stimat th 3dB bandwidth of th nois. Ask for hlp stting up th SA whn you gt to this stp. c) Th SA shows th powr calculatd for all frquncis within th rsolution bandwidth (RBW) for th sttings you hav, P(f)=dBm/RBWHz. From th RBW it calculats P(f)=dBm/Hz assuming P(f) is constant amplitud across th RBW frquncy rang. Rcord th SA rsolution bandwidth (RBW), powr P(f)=(dBm/RBW), and th powr/hz P(f)=dBm/Hz at 10 MHz. d) At what frquncy dos P(f) dbm/hz= P(10 MHz) dbm/hz-3db? This is th 3dB nois bandwidth of th function gnrator. ) What powr in dbm you would masur if th rsolution bandwidth was incrasd by a factor of 10? RC low pass filtr ) Mak a RC low pass filtr using a 0pF capacitor by placing it in paralll with th output of th gnrator. (Rmmbr th gnrator output is 50 ohms). a) Masur th 3 db bandwidth of th filtr using th oscilloscop (hi-z input) and a variabl frquncy sinwav. Compar this to th thortical 3dB bandwidth. b) St th gnrator back to Vp-p nois and look at th signal on th SA. Notic that th 3dB bandwidth of th nois spctrum has bn rducd to th 3db bandwidth of th low pass filtr. c) R-masur th Vp-p and Vrms at th filtr output using th sttings from part 1. Why did th masurd valus chang? (Explain by showing what happns to a signal going through a low pass filtr- LPF using N 0 and H(f)). d) Rduc th 3dB bandwidth of th filtr by using 440pF of capacitanc and rmasur Vp-p and Vrms. Compar ths voltags with th voltags masurd in c. Calculat what you xpct th valus would b for a bandwidth rduction of ½. P watts =(N 0 W/Hz)*(B n) of 13

3 EELE445 Lab 3: Whit nois, ½H(f)½, and a x3 Frquncy Multiplir Coupld LC Bandpass Filtr 3) Build th Coupld Bandpass filtr shown in rfrnc sction and st th scop bandwidth to 0 MHz bandwidth. a) Us th scop to masur th cntr frquncy and bandwidth of th filtr using a swpt sinwav. Rcord th -3dB, -6dB, -10dB, -0dB, and -40dB frquncis. b) St th oscilloscop to us/div with 0 MHz bandwidth, th gnrator output for nois with maximum amplitud. Th nois voltag at th output of th filtr is much lowr sinc th bandwidth of th filtr is small, triggr in th cntr of th scrn, and st th triggr lvl as high as possibl to gt a trac. Stting th triggr for singl trac mod hlps. Not how th signal looks lik a sinwav of th cntr frquncy of th filtr with amplitud that varis at a much slowr rat. This is similar to an AM modulatd wavform (Couch fig 5.1). Ask for hlp from th TA for an xplanation of th wavform and stting th triggr corrctly. c) What is th approximat frquncy of th sin wav? Th is rlatd to th cntr frquncy of th filtr. Estimat th highst frquncy in th nvlop of th sinwav. This is rlatd to th BW of th filtr. X3 Frquncy Multiplir and Filtrd Signals 4) Chang th gnrator to a squar wav with a frquncy qual to th cntr frquncy of th filtr and connct a prob to th input of th filtr to display both th input and output wavforms on th oscilloscop. a) Th output of th filtr should b a sinwav at th cntr frquncy of th filtr. Rcord th amplitud of th output sinwav and compar it to what you would xpct from th squar wav input. Explain any rror. (hint, th filtr allows som of th othr harmonics through) b) Plot th Spctrum of th input and output signals. Considr th first 3 spctral componnts of th output in your for your plot and calculat th distortion of th output sinwav. c) Chang th gnrator frquncy to 1/3 th cntr frquncy of th filtr. Th output of th filtr will b a sinwav at 3 tims th gnrator frquncy with distortion of f/3, 5*f/3, 7*f/3. This principal of frquncy multiplication is usd in communication circuitry in transmittrs and in rcivrs. 3 of 13

4 EELE445 Lab 3: Whit nois, ½H(f)½, and a x3 Frquncy Multiplir REFERENCE SOURCES For Gaussian nois: Th man m, (DC voltag) is zro <v(t)> Th varianc s is th ac nois powr <v(t) >-<v(t)> Th standard dviation s, is th rms nois voltag Th pak to pak valu of th nois voltag is +/- ks whr k is a masur of how Gaussian th nois is. k is typically.5 to 3. Hav you hard of 6s limits bfor? RMS Harmonic Distortion in a sinwav: D k åvn Pdistortion n= % = = Pdsird sin wav V1 100 V 1 is th dsird sinwav amplitud V n ar th amplituds of all th harmonics othr than th dsird sinwav 4 of 13

5 EELE445 Lab 3: Whit nois, ½H(f)½, and a x3 Frquncy Multiplir Coupld Bandpass Filtr PARAMETERS: Cvar = 0p 1Vac 0Vdc V1 R1 50 C1 {Cv ar} C3 1n L1 10uH C {Cv ar} 0 V R 50 0 Gnrator 0 1 Scop or SA R l a t i v R s p o n s Frquncy rspons db d B -60 0Hz MHz 4MHz 6MHz 8MHz 10MHz DB(V(R:))+6 V(R:) Frquncy 5 of 13

6 EELE445 Lab 3: Whit nois, ½H(f)½, and a x3 Frquncy Multiplir R l a t i v 1.0V R s p o n s 0.5V 0V 0.8MHz 1.0MHz 1.MHz 1.4MHz 1.6MHz 1.8MHz.0MHz V(R:)* Frquncy R l a t i v R s p o n s Hz 0.4MHz 0.8MHz 1.MHz 1.6MHz.0MHz.4MHz DB(V(R:)*) Frquncy 6 of 13

7 EELE445 - LAB 3 Studnt Rport Sction Dat Nam 1) Gnrator Nois in Tim and Frquncy Domains a) Masur th Vp-p, Vrms, and VDC magnitud of th nois wavform using th oscilloscop. B sur th nois is not clipping. Hint(us th run stop button) i) Why is it not rading vp-p? Calculat th Vp-p to Vrms ratio. What do w us this ratio for? b) Masurd Spctrum Analyzr (SA) 3dB bandwidth of th nois: Sktch th nois spctrum from 1MHz to 100 MHz using th data you hav. (assum on pol lowpass shap for th nois dnsity.) Idntify points for which you hav data. Provid information for th axis from your SA sttings. Powr dbm RBW: Frquncy 1 of 6

8 EELE445 - LAB 3 Studnt Rport Sction Dat Nam c) Rcord: i) th SA rsolution bandwidth (RBW) ii) powr P(f)=dBm/RBW iii) powr/hz P(f)=dBm/Hz at 10 MHz d) (Sorry, this was a duplicat of 1b) ) Calculat th powr you would masur for Cii) if th rsolution bandwidth was incrasd by a factor of 10? ) RC low pass filtr a) Masur th 3 db bandwidth of th filtr using th oscilloscop (hi-z input) and a variabl frquncy sinwav. Compar this to th thortical 3dB bandwidth. b) St th gnrator back to Vp-p nois and look at th signal on th SA. Notic that th 3dB bandwidth of th nois spctrum has bn rducd by th 3db bandwidth of th low pass filtr. of 6

9 EELE445 - LAB 3 Studnt Rport Sction Dat Nam c) R-masur th Vp-p and Vrms at th filtr output using th sttings from part 1a. Why did th masurd valus chang? (Explain by showing what happns to a signal going through a low pass filtr- LPF using N 0 and H(f)) d) Rduc th 3dB bandwidth of th filtr by ½ by using 440pF of capacitanc and rmasur Vp-p and Vrms. Compar ths voltags with th voltags masurd in c by using your voltag valus masurd in c to calculat what you xpct th valus to b for a bandwidth rduction of ½. Rmmbr P watts =N 0 *B n rducing B n to B n / 1 should rduc th rms voltag by. How closly do th masurd voltags compar to th idal voltag? Calculat th rror. 3) Coupld LC Bandpass Filtr a) Rcord th -3dB, -6dB, -10dB, -0dB, and -40dB frquncis. Mak a tabl and a sktch of th filtr rspons idntifying your masurd valu valus. Lvl db Lowr Frquncy Uppr Frquncy Nots: 0 db -3 db -6 db -10 db -0 db -40 db 3 of 6

10 EELE445 - LAB 3 Studnt Rport Sction Dat Nam db 0 db Filtr Frquncy Rspons Frquncy b) Us what you found to answr c) c) What is th approximat frquncy of th sin wav? This is rlatd to th cntr frquncy of th filtr. Estimat th highst frquncy in th nvlop of th sinwav. This is rlatd to th BW of th filtr. 4) X3 Frquncy Multiplir and Filtrd Signals a) Th output of th filtr should b a sinwav at th cntr frquncy of th filtr. Rcord th amplitud of th output sinwav and compar it to what you would xpct from th squar wav input. Explain any rror. (hint, th filtr allows som of th othr harmonics through) Thortical amplitud of fundamntal Vp-p squar wav from prvious labs: Masurd amplitud from oscilloscop: Calculatd rror: Explanation of rror: 4 of 6

11 EELE445 - LAB 3 Studnt Rport Sction Dat Nam 5 of 6

12 EELE445 - LAB 3 Studnt Rport Sction Dat Nam b) Plot th Spctrum of th input and output signals. Considr th first 3 spctral componnts of th output plot and calculat th distortion of th output sinwav. You may us th following tabl for your data. n Input dbv Output dbv Ouput V rms nots 1 (fundamntal) Not that th amplitud diffrnc in db of th input and output lvls is qual to th insrtion loss of th filtr Amplitud Filtr Input and Output Spctrum Frquncy 6 of 6

13 EELE445 - LAB 3 Studnt Rport Sction Dat Nam c) Chang th gnrator frquncy to 1/3 th cntr frquncy of th filtr. Th output of th filtr will b a sinwav at 3 tims th gnrator frquncy with distortion of f/3, 5*f/3, 7*f/3. This principal of frquncy multiplication is usd in communication circuitry in transmittrs and in rcivrs. EELE445 - LAB 3 Studnt Rport Sction Dat Nam 7 of 6