Diode Applications Diode Switching As we have already seen the diode can act as a switch Forward biased or reverse biased - On or Off. Voltage Rectifier A voltage rectifier is a circuit that converts an AC voltage to a DC voltage. AC Voltage An AC voltage, as represented by a sine wave, is one where the polarity of the voltage changes (and the current flow reverses) in a periodic manner. This waveform has RMS, Peak, and Peak-Peak values. It also has an average value of 0 volts - V Avg = 0 V. Note: Average value is what a voltmeter reads when set to DC volts. DC Voltage A DC voltage is one where the polarity of the voltage does not change (and the current flow does not reverse) in a periodic manner. The diagram below left shows a constant DC voltage while at right there is a non-constant DC voltage.
Half Wave Rectifier A Half Wave rectifier can be constructed using a single diode as shown in the circuit. An AC voltage is connected to a transformer and the transformer output voltage is rectified by a single diode. The secondary voltage from the transformer has a voltage that can be described as V S,Pk. During the positive half cycle of the transformer secondary voltage, the diode is forward biased and turns ON. During the negative half cycle of the transformer secondary voltage, the diode is reverse biased and turns OFF. The waveform shown below is called the Half Wave Rectified output waveform for this circuit. The peak load voltage V L,Pk is the voltage across the load resistor. The peak load voltage V L,Pk = V S,Pk - 0.7 V Question Does this Half Wave Rectified output waveform represent a DC or an AC voltage? Average Value As the waveform is always positive, the Half Wave Rectified output load voltage waveform has a nonzero average value. This DC or average value can be calculated as V L,Avg = V L,DC = V L,Pk /π
Example 1. A transformer with a turns ratio of 1:12 has a 120 VAC connected to the primary. The secondary voltage is connected to a Half Wave rectifier circuit with a 1 kω load resistor. What is the RMS secondary voltage? What is the peak load voltage? What is the peak secondary voltage? What is the peak load current? What is the average load voltage? Answers RMS secondary voltage V S,RMS = V P x 1/12 = 120 V x 1/12 = 10 V RMS Peak secondary voltage V S,Pk = 10 V x 1.41 = 14.1 V Pk 2 = 1.41 Peak load voltage Peak load current Average load voltage V L,Pk = V S,Pk - 0.7 = 14.1-0.7 = 13.4 V Pk I L,Pk = V L,Pk /1 kω = 13.4 ma Pk V Avg = V L,Pk /π = 13.4 V Pk/π = 4.3 V DC Frequency of Load Voltage waveform If the voltage connected to the primary of the transformer is 60 Hz then the frequency of Load Voltage waveform will also be 60 Hz. Capacitive Filtering The rectifier circuit has created a pulsating DC voltage at the load. This can be improved to a more constant DC voltage by the use of a filter capacitor. The capacitor charges up during the time when the diode is conducting and discharges during the time the diode is off. The amount of discharge depends on the value of the load resistor and the capacitor the larger the values of R and C the smaller the amount of discharge will be and the filtered waveform will be closer to a constant value.
Ripple Voltage The filtering action of the capacitor produces an output (load) voltage waveform that is called a Ripple Voltage. The ripple voltage is measured as a Peak-Peak value V ripple,p-p. The ripple voltage is defined in terms of the maximum and minimum values of the ripple voltage waveform. V ripple,p-p = V max - V min The RMS value of the ripple voltage is V ripple,rms = V ripple,p-p / 2 3 The Average or DC value of the load voltage is V L,DC = V L,Avg = (V max + V min )/2 The frequency of the ripple voltage waveform is 60 Hz. Example 2. A filtered output load voltage has a ripple voltage with V max = 13.4 V and V min = 11.2 V. What are the values of V ripple,p-p, V ripple,rms and V L,Avg (V L,DC ). V ripple,p-p = V max - V min = 13.4 V - 11.2 V = 2.2 V P-P V ripple,rms = V ripple,p-p / 2 3 = 2.2 V P-P/ 2 3 = 0.64 V RMS V L,DC = V L,Avg = (V max + V min )/2 = (13.4 V + 11.2 V)/2 = 12.3 V DC Capacitor Size If the size of the capacitor is increased the ripple voltage will decrease. At some point the capacitor will be sufficiently large that the average DC load voltage will increase until it is approximated by the peak load voltage. In practice capacitor size is not increased excessively as there are other ways to help reduce the size of the ripple voltage. V L,DC V L,Pk
Percent Ripple The value of the ripple voltage alone is not sufficient by itself to accurately describe the circuit performance. A better descriptor is percent ripple which relates the ripple voltage to the average or DC load voltage. Percent Ripple (% ripple) = V ripple,p-p / V L,DC x 100% Consider these two examples. 1. V L,DC = 5.0 V V ripple,p-p = 1.0 V P-P % ripple = 1.0 V / 5.0 V x 100% = 20 % 2. V L,DC = 25 V V ripple,p-p = 1.0 V P-P % ripple = 1.0 V / 25 V x 100% = 4 % Which example has the better ripple performance? Full Wave Rectifier 2 diode circuit The two drawings below show a full wave rectifier. You should satisfy yourself that they are equivalent representations. Note: The transformer for this rectifier circuit requires a center tap connection.
Full Wave Rectified Waveform The full wave rectified load voltage waveform is shown. Each diode in the circuit contributes one half of the output waveform. The center tap of the transformer divides the secondary voltage in half so the voltage connected to each diode is V S,Pk /2. The peak load voltage is now V L,Pk = V S,Pk /2-0.7 V The average load voltage is now V L,Avg = V L,DC = 2 V L,Pk /π The frequency of this waveform is double that of the half wave rectifier. If the primary frequency is 60 Hz then the frequency of the load waveform is 120 Hz. Example 3. A transformer with a 1:4 turns ratio is connected to 120 VAC and a full wave rectifier (2 diode) circuit. What is the RMS and Peak secondary voltage? What is the peak load voltage? What is the average load voltage? Answers V S = V P x 1/4 = 120 VAC x 1/4 = 30 V RMS = 42.2 V Pk V L,Pk = V S,Pk /2-0.7 = 42.4 V/2-0.7 = 21.2-0.7 = 20.5 V Pk V L,Avg = V L,DC = 2 V L,Pk /π = 2 x (20.5)/π = 13.1 V DC
Full Wave Rectifier Bridge Rectifier circuit As with the 2 diode full wave rectifier the circuit for the bridge rectifier circuit can be represented in several but equivalent ways. Each circuit however requires 4 diodes connected in a bridge circuit arrangement. Circuit Operation On the positive half cycle of the secondary voltage two of the bridge diodes (D 3 and D 1 ) are forward biased and conduct as shown below left. On the negative half cycle of the secondary voltage two of the bridge diodes (D 4 and D 2 ) are forward biased and conduct as shown below right. The frequency of this waveform is also double that of the half wave rectifier. If the primary frequency is 60 Hz then the frequency of the load waveform is 120 Hz. The voltage connected to each diode is V S,Pk. The peak load voltage is now V L,Pk = V S,Pk - 1.4 V
The average load voltage is now V L,Avg = V L,DC = 2 V L,Pk /π Example 4. A transformer with a 1:4 turns ratio is connected to 120 VAC and a full wave Bridge rectifier circuit. Answers What is the RMS and Peak secondary voltage? What is the peak load voltage? What is the average load voltage? V S = V P x 1/4 = 120 VAC x 1/4 = 30 V RMS = 42.2 V Pk V L,Pk = V S,Pk - 1.4 = 42.4 V - 1.4 V = 41.0 V Pk V L,Avg = V L,DC = 2 V L,Pk /π = 2 x (41.0)/π = 27.3 V DC Bridge Rectifier Component The bridge rectifier circuit configuration is very popular and rather than using 4 discrete diodes to build it, manufacturers make a device that incorporates the 4 diodes in a single component. These devices can often be attached to a heat sink and can handle larger currents. Two examples are shown below.
Capacitive Filtering As with the half wave rectifier a capacitor can be added (for either of the full wave rectifier circuits) in parallel with the load resistor to help smooth the rectified waveform. The ideas and definitions developed earlier about the ripple voltage still apply to this waveform. V ripple,p-p = V max - V min The RMS value of the ripple voltage is V ripple,rms = V ripple,p-p / 2 3 The Average or DC value of the load voltage is V L,DC = V L,Avg = (V max + V min )/2 See the Summary of Rectifiers handout on the course web site