V1 is 50 mv at 88Mhz V2 is 7.73 Volts dc o Real circuit has supply voltage of 7.73 due to Ir drop across 220 ohm R25 and 100 ohm R9 Ir25 = (8.85-7.75V)/220 ohm = 5 ma Ir9 = (7.75-7.37V)/100 ohm = 3.8 ma Purpose and Function The incoming radio waves are amplified by the FM RF amplifier. 1 Theory and Design The RF amplifier and the oscillator are the only two resonant circuits that change when the radio is tuned for different stations. Since a radio station may exist 10.7MHz above the oscillator frequency, it is important that the RF stage rejects this station and selects only the station 10.7MHz below the oscillator frequency. The frequency of the undesired station 10.7MHz above the oscillator is called the image frequency. Since this FM receiver has an RF amplifier, the image frequency is reduced significantly. 1 William R. Robinson Jr. p1of 10
Calculated Basically a common base amplifier 2 with tank circuit in place of Rc which is used for tuning FM Radio range is 88 MHz to 108 MHz The oscillation frequency is determined by Ceff and L1_2 Ceff = C1 in series with C6 C6 = 33 pf C1 is variable from a BC-88 is variable from 23 up to 44 pf 3 C1* C10 o Ceff C1 C10 o Ceff_min = 13.5pF o Ceff_max = 18.9pf 1 4 Re sonate Fr 2 LC 1 L 2 (2 Fr _ min) * Ceff _ max o L1_2 = 1/(6.28 * 88 Mhz) 2 * (18.9)pf o L1_2= 173 nh Now with the fixed inductance of 173 nh we compute Ceff_min required for the higher frequency and see if it is within C1 s range 1 Ceff _ min 2 (2 Fr _ max) * L Ceff = 1/(6.28* 108 Mhz) 2 * 173 nh Ceff = 12.5pf note this is within the range computed above for the real circuit Inductance The inductor is formed from a short piece of wire wound into a coil Inductance of a short air core cylindrical coil in terms of geometric parameters: 2 r N 5 o L( uh ) 9r 10l L = inductance in µh r = outer radius of coil in inches l = length of coil in inches N = number of turns This formula is most accurate when the coil length (A) is greater than 0.67r and the frequency is less than10 MHz. As the frequency goes above 10MHz, the formula becomes less accurate, because parasitics dominate the circuit. 5 William R. Robinson Jr. p2of 10
The wire is about.029 inches in cross section diameter, with 6 turns formed into a coil about.26 in. in Diameter L =(0.13 2 *8 2 )/(9 * (0.13) + 10 * (0.029*6) L= (1.08)/(1.125 + 1.5) L= 309nH This is a quit a bit more than calculated above but can be decreased during tuning by spreading the coils After tuning the Inductance was measured at 230 nh which is close to the value calculated above DC Bias The impedance of L1/Ceff is 0 at dc, therefore Vc = Vcc o Vc = 7.73V Vb = Vcc*R2/(R2+R1) o Vb = 7.73 * 6.8K(6.8K+22K) = 1.8V Ve = Vb 0.7V o Ve = 1.8-0.7 = 1.1V Gain Predicting voltage gain for the common-base amplifier configuration is quite difficult, and involves approximations of transistor behavior that are difficult to measure directly. Unlike the other amplifier configurations, where voltage gain was either set by the ratio of two resistors (common-emitter), or fixed at an unchangeable value (common-collector), the voltage gain of the common-base amplifier depends largely on the amount of DC bias on the input signal. As it turns out, the internal transistor resistance between emitter and base plays a major role in determining voltage gain, and this resistance changes with different levels of current through the emitter. 6 William R. Robinson Jr. p3of 10
Simulation Except for very low values, load has little effect on the output as shown in the simulation below o For Rload = 1K to 10K in 2K steps FM_RF_amp-Transient-4-Sweep-Graph v(nout)[0] v(nout)[1] v(nout)[2] v(nout)[3] v(nout)[4] 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 40.300u 40.302u 40.304u 40.306u 40.308u 40.310u Time 40.312u 40.314u 40.316u 40.318u 40.32 Rload was picked as the input load of the 2nd If amp o Xin of Q3 ~ Xc5 + R7//R8//hfe*R11 2 1 Xc 2 FC Xc5 = 2*pi*108Mhz*470pf Xc5 = 3 ohms and is negligible Xin Q3 ~ 6.8K//22K//100*1.8K Xin Q3 ~ 5K (load for model) o But this goes through the transformer L1_2 with a turns ration of 6:2 Zin = Zin Q5 turns_ratio 2 Zin = 5K (6/2) 2 Zin = 45K (load seem by Q1) Values work nearly as calculated o With C1 = 18.9pf and L1= 173h Note the high gain at resonance of 82.9 Mhz William R. Robinson Jr. p4of 10
vm(nout) FM_RF_amp-Small Signal AC-6-Graph 550.000 500.000 450.000 400.000 350.000 300.000 250.000 200.000 150.000 100.000 50.000 0.0-50.000 50.000M 60.000M 70.000M 80.000M 90.000M 100.000M110.000M120.000M130.000M 140.000M 150.000M 160.000M 170.000M 180.000M 190.000M 200.00 o With C1 = 13.5pf and L1 = 173h = 97.8 Mhz Series1 Series2 7.000 6.500 6.000 5.500 5.000 4.500 4.000 3.500 3.000 2.500 2.000 1.500 1.000 500.000m 0.0-500.000m 0.0 50.000M 100.000M 150.000M 200.000M 250.000M 300.000M C3 really narrows the band width again at a cost of about half the gain o With C1 = 18.9pf and L1= 173h and NO C3 vm(nout) FM_RF_amp-Small Signal AC-8-Graph 1.100 1.050 1.000 950.000m 900.000m 850.000m 800.000m 750.000m 700.000m 650.000m 600.000m 550.000m 500.000m 450.000m 400.000m 350.000m 300.000m 250.000m 200.000m 50.000M 60.000M 70.000M 80.000M 90.000M 100.000M110.000M120.000M130.000M 140.000M 150.000M 160.000M 170.000M 180.000M 190.000M 200.00 DC Bias William R. Robinson Jr. p5of 10
Very close to calculated see Comparison below Gain Gain = 9.5-6/.05 = 70 o 20 log(70) = 36.9 db Bandwidth With tank circuit 1.5Mhz 87.629 86.096 Without tank circuit > 150Mhz o With L1 and Ceff replaced by the same value as R3 (~ unity gain) we see that the amp half power point is out to 150 Mhz FM_RF_amp-Small Signal AC-9-Graph vm(nout) 28.500 28.000 27.500 27.000 26.500 26.000 25.500 25.000 24.500 24.000 23.500 23.000 22.500 22.000 50.000M 60.000M 70.000M 80.000M 90.000M 100.000M110.000M120.000M130.000M 140.000M 150.000M 160.000M 170.000M 180.000M 190.000M 200.00 William R. Robinson Jr. p6of 10
DC Bias Good correlation to spice Gain Bandwidth Unable to measure gain etc as do not have a signal generator which goes this high RF AMP Output at Q1C measured with radio tuned to Classy 92.1 Mhz (no signal Generator) o With the local oscillator shorted out RF at about 30 mvp-p o RF AMP Output at Q1C without the local oscillator shorted out. Note obvious feedback from local oscillator at 92.1Mhz Rf + 10.7Mhz IF = 102.8Mhz scope measures 103.2Mhz About 140mVp-p William R. Robinson Jr. p7of 10
William R. Robinson Jr. p8of 10
Comparison Gain db Bandwidth Mhz Real-Measured Simulation Calculated Documentation Not Measurable 36.9 N/A Not given No RF generator (emitter-collector) Not Measurable 1.5 N/A Not given No RF generator L uh 230 173 173 N/A Vc 7.4 7.73 7.73 7.0 Vb 1.7 1.7 1.8 1.6 Ve 1.0 1.1 1.1 0.9 William R. Robinson Jr. p9of 10
References 1. UNKNOWN, Model AM/FM-108TK 14 Transistors, 5 diodes Assembly and Instruction Manual, (ELENCO, 2004) 2. Gingrich, Doug, The common Base Amplifier, (1999), http://www.piclist.com/images/ca/ualberta/phys/www/http/~gingrich/phys395/notes/n ode87.html, online, accessed 2008. 3. http://www.oselectronics.com/ose_p98.htm, online, accessed 2008. Miniature Poly-film Variable Tuning Capacitor For AM & FM Bands Ideal variable tuning capacitor for miniature circuitry and use as exact-duplicate replacement in current transistor receivers. Tunes AM Band from 540Khz to 1600Khz and FM band from 88Mhz to 108Mhz. Rotates through a full 180 Maximum capacity: Antenna section AM 21-152PF, Oscillator Section AM, 10-74PF. Antenna section FM 23-44PF, Oscillator Section FM, 14-23PF Trimmer capacity: variable to over 12PF. Trimmer adjustment on rear of case. Completely enclosed to clear polyethylene plastic case to protect plates. Includes calibrated dial, screw, and knob. Small size, 3/4" Square x 1/2" Deep. 4. UNKNOWN, The ARRL Handbook For Radio Communications, (ARRL 2008) p4.47, (Eq. 110) 5. UNKNOWN, Air Coil Inductors, (CWS BYTE MARK), http://www.coilws.com/c_winding_main/air%20coil%20inductors.pdf, online, accessed 2008. 6. UNKNOWN, The common-base Amplifier, http://www.allaboutcircuits.com/vol_3/chpt_4/7.htm, online, accessed 2008.l William R. Robinson Jr. p10of 10