4Sine WaveThe sine wave is a common type of alternating current (ac) and alternating voltage.The time required for a sine wave to complete one full cycle is called the period (T).Frequency ( f ) is the number of cycles that a sine wave completes in one second.The more cycles completed in one second. The higher the frequency.Frequency is measured in hertz (Hz)Relationship between frequency ( f ) and period (T) is:f = 1/T
5Peak-to-Peak / Average / RMS The rms (root mean square) value of a sinusoidal voltage is equal to the dc voltage that produces the same amount of heat in a resistance as does the sinusoidal voltage.Vrms = 0.707VpIrms = 0.707IpThe peak-to-peak value of a sine wave is the voltage or current from the positive peak to the negative peak.The peak-to-peak values are represented as:Vpp and IppWhere: Vpp = 2Vp and Ipp = 2Ip
8Half-wave Rectifier For Silicon VBar = 0.7 V Note that the frequency stays the sameStrength of the signal is reducedVavg = Vp(out)/p = x Vp(out) [31.8 % of Vp]Vp(out) = Vp(in) – VBarFor Silicon VBar = 0.7 VHalf-waveRectifierVp(out)Vp(in)Vavg2p
9Half-wave Rectifier - Example Draw the output signalVp(out) = Vp(in) – 0.7Vavg = 99.3/pWhat happens to thefrequency?Peak Inverse Voltage (PIV)The peak voltage at which the diode is reverse biasedIn this example PIV = Vp(in)-Hence, the diode must be rated for PIV = 100 VOutput:
10Transformers (Review) Transformer: Two inductors coupled together – separated by a dielectricWhen the input magnetic field is changing voltage is induced on the second inductorThe dot represents the + (voltage direction)Applications:Step-up/downIsolate sourcesTurns ratio (n)n = Sec. turns / Pri. turns = Nsec/NpriVsec = n. Vpridepending on value of n : step-up or step-downCenter-tapped transformerVoltage on each side is Vsec/2
11Half-wave Rectifier - Example Assume that the input is a sinusoidal signal with Vp=156 V & T = 2 msec; assume Nsec:Npri = 1:2Draw the signalFind turns ratio;Find Vsec;Find Vout.n = ½ = 0.5Vsec = n.Vpri = 78 VVout = Vsec – 0.7 = 77.3 V78-0.7
12Full-wave Rectifier Note that the frequency is doubled Vavg = 2Vp(out)/p = x Vp(out)
13Full-wave Rectifier Circuit Center-tapped full-wave rectifierEach half has a voltage = Vsec/2Only one diode is forward biased at a timeThe voltages at different halves are opposite of each other
14Full-wave Rectifier Circuit Center-tapped full-wave rectifierEach half has a voltage = Vsec/2Only one diode is forward biased at a timeThe voltages at different halves are opposite of each other
16Full-wave Rectifier - Example Assuming a center-tapped transformerFind the turns ratioFind VsecFind VoutFind PIVDraw the Vsec and VoutWhat is the output freq?Vsecn=1:2=0.5Vsec=n*Vpri=25Vout = Vsec/2 – 0.7PIV = Vsec-0.7=24.3 V
17Full-wave Rectifier - Multisim XFrmr can be virtual or realUse View Grapher to see the details of your resultsThe wire-color can determine the waveform colorMake sure the ground is connected to the scope.
18Bridge Full-wave Rectifier Uses an untapped transformer larger VsecFour diodes connected creating a bridgeWhen positive voltage D1 and D2 are forward biasedWhen negative voltage D3 and D4 are forward biasedTwo diodes are always in series with the loadVp(out) = Vp(sec) – 1.4VThe negative voltage is invertedThe Peak Inverse Voltage (PIV)PIV=Vp(out)+0.7
19Bridge Full-wave Rectifier - Example Assume 12 Vrms secondary voltage for the standard 120 Vrms across the primaryFind the turns ratioFind Vp(sec)Show the signal direction when Vin is positiveFind PIV rating120Vrmsn=Vsec/Vpri = 0.110:1Vp(sec) = (0.707)-1 x Vrms = 1.414(12)=17 VVp(out) = V(sec) – ( ) = 15.6 V through D1&D2PIV = Vp(out) = 16.3 VNote: Vp-Vbr ; hence, always convert from rms to Vp
20Bridge Full-wave Rectifier - Comparison 120VrmsVp(2)=Peak secondary voltage ; Vp(out) Peak output voltage ; Idc = dc load currentMake sure you understand this!
25FiltersRipple voltage depends on voltage variation across the capacitorLarge ripple means less effective filterpeak-to-peak ripple voltage
26Filters Too much ripple is bad! Ripple factor = Vr (pp) / VDC Vr (pp) = (1/ fRLC) x Vp(unfiltered)VDC = (1 – 1/ fRLC) x Vp(unfiltered)
27Diode Limiting What is Vout? Vout+ = Vin (RL)/(RL+R1) = 9.09 Forward biased when positiveReverse biased when negative,hence voltage drop is only -0.7So how can we change the offset?
28Diode Limiting – Changing the offset Negative limiterRemember:When positive voltage reverse biased No current no clipping!Positive limiterWhat if we mix these together?
29Diode LimiterWhen the input signal is positive D1 is reversed biased; acting as positive limiterPos. Limiter+VBIAS+0.7-VBIAS-0.7
30Diode Clamper It adds a dc level When the input voltage is negative, the capacitor is chargedInitially, this will establish a positive dc offsetNote that the frequency of the signal stays the sameRC time constant is typically much larger than 10*(Period)Note that if the diode and capacitor are flipped, the dc level will be negativeOutput: