Half-Wave Rectifier

 

 

CLIPPERS 


Clippers are networks that employ diodes to “clip” away a portion of an input signal without distorting the  remaining part of the applied waveform. 


There are two general categories of clippers: series and parallel. The series configuration is defined as one  where the diode is in series with the load, whereas the parallel variety has the diode in a branch parallel to  the load. 


Series configuration 


The response of the series configuration of Fig. 2.68a to a variety of alternating waveforms is provided in  Fig. 2.68b. 



The addition of a dc supply to the network as shown in Fig. 2.69 can have a pronounced effect on the  analysis of the series clipper configuration.  



The response is not as obvious because the dc supply can aid or work against the source voltage.  For analyzing networks such as the type in Fig. 2.69, one must follow the necessary steps 


1. Take careful note of where the output voltage is defined. 


2. Try to develop an overall sense of the response by simply noting the “pressure” established by each  supply and the effect it will have on the conventional current direction through the diode. 3. Determine the applied voltage (transition voltage) that will result in a change of state for the diode  from the “off” to the “on” state.


4. It is often helpful to draw the output waveform directly below the applied voltage using the same  scales for the horizontal axis and the vertical axis. 


EXAMPLE 2.18 Determine the output waveform for the sinusoidal input of Fig. 2.74. 


Solution: 


Step 1: The output is again directly across the resistor R.  


Step 2: The positive region of v i and the dc supply are both applying “pressure” to turn the diode on. The  result is that we can safely assume the diode is in the “on” state for the entire range of positive voltages for  v i. Once the supply goes negative, it would have to exceed the dc supply voltage of 5 V before it could turn  the diode off. 


Step 3: The transition model is substituted in Fig. 2.75, and we find that the transition from one state to the  other will occur when 



Step 4: In Fig. 2.76a horizontal line is drawn through the applied voltage at the transition level. For voltages  less than -5 V the diode is in the open-circuit state and the output is 0 V, as shown in the sketch of v o. Using  Fig. 2.76, we find that for conditions when the diode is on and the diode current is established the output  voltage will be the following, as determined using Kirchhoff’s voltage law



Parallel Configuration 


The network of Fig. 2.81 is the simplest of parallel diode configurations with the output for the same inputs  of Fig. 2.68. The analysis of parallel configurations is very similar to that applied to series configurations,  as demonstrated in the next example.



example Determine v o for the network of Fig. 2.82. 



Solution:  


Step 1: In this example the output is defined across the series combination of the 4-V supply and the diode,  not across the resistor R. 


Step 2: The polarity of the dc supply and the direction of the diode strongly suggest that the diode will be  in the “on” state for a good portion of the negative region of the input signal. In fact, it is interesting to note  that since the output is directly across the series combination, when the diode is in its short-circuit state the  output voltage will be directly across the 4-V dc supply, requiring that the output be fixed at 4 V. In other  words, when the diode is on the output will be 4 V. Other than that, when the diode is an open circuit, the  current through the series network will be 0 mA and the voltage drop across the resistor will be 0 V. That  will result in vo = vi whenever the diode is off.  


Step 3: The transition level of the input voltage can be found from Fig. 2.83 by substituting the short-circuit  equivalent and remembering the diode current is 0 mA at the instant of transition.  



The result is a change in state when vi = 4 V


Step 4: In Fig. 2.84the transition level is drawn along with vo = 4 V when the diode is on. For vi > 4 V, vo = 4 V, and the waveform is simply repeated on the output plot 



Clamper 


A clamper is a network constructed of a diode, a resistor, and a capacitor that shifts a waveform to a different  dc level without changing the appearance of the applied signal. 


Additional shifts can also be obtained by introducing a dc supply to the basic structure. 


Clamping networks have a capacitor connected directly from input to output with a resistive element in  parallel with the output signal. The diode is also in parallel with the output signal but may or may not have  a series dc supply as an added element. 



There is a sequence of steps that can be applied to help make the analysis straightforward. 


Step 1: Start the analysis by examining the response of the portion of the input signal that will forward bias  the diode.  


Step 2: During the period that the diode is in the “on” state, assume that the capacitor will charge up  instantaneously to a voltage level determined by the surrounding network.


Step 3: Assume that during the period when the diode is in the “off” state the capacitor holds on to its  established voltage level. 


Step 4: Throughout the analysis, maintain a continual awareness of the location and defined polarity for vo to ensure that the proper levels are obtained. 


Step 5: Check that the total swing of the output matches that of the input. 


EXAMPLE 2.22 Determine v o for the network of Fig. 2.93 for the input indicated. Solution 


Note that the frequency is 1000 Hz, resulting in a period of 1 ms and an interval of 0.5 ms between levels.  The analysis will begin with the period t1 to t2 of the input signal since the diode is in its short-circuit state.  For this interval the network will appear as shown in Fig. 2.94. 



The output is across R, but it is also directly across the 5-V battery if one follows the direct connection  between the defined terminals for vo and the battery terminals. The result is vo = 5 V for this interval.  Applying Kirchhoff’s voltage law around the input loop results in



The capacitor will therefore charge up to 25 V. In this case the resistor R is not shorted out by the diode,  but a Thévenin equivalent circuit of that portion of the network that includes the battery and the resistor  will result in RTh = 0 Ω with ETh = V = 5 V. For the period t2 to t3 the network will appear as shown in Fig.  2.95. 



The open-circuit equivalent for the diode removes the 5-V battery from having any effect on vo , and  applying Kirchhoff’s voltage law around the outside loop of the network results in 



The time constant of the discharging network of Fig. 2.95 is determined by the product RC and has the  magnitude 



The total discharge time is therefore 5τ = 5(10 ms) = 50 ms. Since the interval t 2 to t3 will only last for 0.5  ms, it is certainly a good approximation that the capacitor will hold its voltage during the discharge period  between pulses of the input signal. The resulting output appears in Fig. 2.96 with the input signal. Note that  the output swing of 30 V matches the input swing as noted in step 5.



Zener Diode as a Voltage Regulator 


In the reverse bias of a zener diode, there is a voltage which remains almost constant even with large  changes in current. This ability of the zener diode to control itself can be used to great effect to regulate or  stabilize a voltage source against supply or load variations. The fact that the voltage across the diode in the  breakdown region is almost constant turns out to be an important characteristic of the zener diode as it can  be used in the simplest types of voltage regulator applications. 


A voltage regulator is an electronic circuit that provides a stable DC voltage independent of the load current,  temperature and AC line voltage variations. The function of a voltage regulator is to provide a constant  output voltage to a load connected in parallel with it in spite of the ripples in the supply voltage or variations  in the load current. A zener diode will continue to regulate its voltage until the diodes holding current falls  below the minimum value in the reverse breakdown region. 


A Zener diode of break down voltage VZ is reverse connected to an input voltage source Vi across a load  resistance RL and a series resistor R.  


Zener Diodes can be used to produce a stabilized voltage output with low ripple under varying load current  conditions. By passing a small current through the diode from a voltage source, via a suitable current  limiting resistor (R), the zener diode will conduct sufficient current to maintain a voltage drop of Vout. The  zener diode is connected with its cathode terminal connected to the positive rail of the DC supply so it is  reverse biased and will be operating in its breakdown condition. The load is connected in parallel with the  zener diode, so the voltage across RL is always the same as the zener voltage, ( VRL = VZ ). There is a  minimum zener current for which the stabilization of the voltage is effective and the zener current must  stay above this value operating under load within its breakdown region at all times. The upper limit of  current is of course dependent upon the power rating of the device. The supply voltage Vi must be greater  than VZ. 


One small problem with zener diode stabilizer circuits is that the diode can sometimes generate electrical  noise on top of the DC supply as it tries to stabilize the voltage. Normally this is not a problem for most  applications but the addition of a large value decoupling capacitor across the Zener’s output may be required  to give additional smoothing. 


To summarize, a zener diode is always operated in its reverse biased condition. As such a simple voltage  regulator circuit can be designed using a zener diode to maintain a constant DC output voltage across the  load in spite of variations in the input voltage or changes in the load current. The stabilized output voltage  is always selected to be the same as the breakdown voltage VZ of the diode.









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