This course introduces students to the basic components of electronics: diodes, transistors, and op amps. It covers the basic operation and some common applications.

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From the course by Georgia Institute of Technology

Introduction to Electronics

317 ratings

Georgia Institute of Technology

317 ratings

This course introduces students to the basic components of electronics: diodes, transistors, and op amps. It covers the basic operation and some common applications.

From the lesson

Diodes Part 2

Learning Objectives: 1. Examine additional applications of the diode. 2. Make use of voltage transfer characteristics to analyze diode circuit behavior.

- Dr. Bonnie H. FerriProfessor

Electrical and Computer Engineering - Dr. Robert Allen Robinson, Jr.Academic Professional

School of Electrical and Computer Engineering

Welcome back to Electronics, this is Dr. Robinson.

Â In this lesson, we're going to look at what are called Full-Wave Rectifiers.

Â In the previous lesson, you were introduced to diode half-wave rectifiers.

Â We didn't analyze the behavior of a particular half-wave rectifier circuit,

Â considering the diodes to be both ideal and non-ideal.

Â Our objectives for today are to introduce full-wave rectifiers.

Â We'll then examine their behaviors for sinusoidal inputs, and then,

Â analyze a diode full-wave rectifier circuit.

Â Now remember, our definition for

Â a rectifier is a non-linear device that modifies an input voltage,

Â such that the output voltage is greater than or less than, some threshold voltage.

Â Let's look at what that definition means graphically.

Â Here I've drawn a box to represent our full-wave rectifier.

Â We are applying as an input a sinusoidal varying voltage.

Â And I've drawn two possible outputs of the full-wave rectifier.

Â Let's look at this output first, and

Â determine it's relationship, with the input voltage.

Â You can see that when the input voltage is positive,

Â the output voltage is exactly equal to the input voltage.

Â But when the input voltage is negative,

Â the output voltage is equal to the input voltage multiplied by minus one.

Â This wave form is known as a positive full-wave rectified sine wave.

Â Positive because it's entirely greater than out threshold voltage of zero volts.

Â And full-wave, because the output is nonzero, for

Â every half period of the input.

Â Now remember for the half wave rectifier, our output was nonzero only for

Â every other half period of the input.

Â The output voltage waveform down here is known as a negative full-wave

Â rectified sine wave.

Â Negative because it's entirely below the threshold voltage of zero volts.

Â And full-wave rectified again, because the output is nonzero for

Â every half period of the input.

Â So here I've defined the behavior of a positive full-wave rectifier in terms of

Â rules that we can apply to the input.

Â If the input is greater than or equal to 0, the output is equal to the input.

Â However, if the inputs is less than 0,

Â the output is equal to the input times minus 1.

Â Now let's look at a circuit that may be used to implement a full-wave rectifier.

Â You may recognize this depology.

Â This is a wheatstone bridge depology,

Â where the elements of the bridge are diodes.

Â And in this case, the diodes are considered to be ideal.

Â A V in is a positive voltage, it will attempt to push current,

Â from its positive terminal, through the circuit, back to its negative terminal.

Â However, in this circuit, the paths the current can flow in,

Â are limited by the direction of the diodes.

Â So let's say current is,

Â is being pushed out of the positive terminal of the voltage source.

Â We can see that the current can't flow in this direction through D4 because of

Â its direction.

Â So the current must flow, through this branch, down through D1.

Â It's then forced to flow through the resistor because of the direction of D3.

Â Now at this node, we, if we just look at directions, it would appear that

Â current could flow both in this direction through D4, and this direction through D2.

Â However, we know that the voltage has decreased from this node,

Â by 1IR drop to get to this node.

Â Which means that this voltage is less than this voltage.

Â So D4 would be off, or reverse biased.

Â So the current that's coming through this branch through the resistor R,

Â must flow down through D2 and back to the minus side, of the input source.

Â So, when V in is positive, we can replace D1 and

Â D2 by short circuits, and D4 and D3 by open circuits.

Â And I've redrawn the circuit here, with those changes.

Â Now we can perform a similar analysis when V in is negative, and

Â arrive at this result.

Â Now the key to the operation of this circuit is to notice that, in this circuit

Â we know that current must be flowing in this direction, because of the diodes.

Â So current is flowing from the positive side of V out to the negative side of V

Â out which means V out has a positive voltage.

Â Now in this circuit, when V in is negative, remember for a negative

Â voltage we can consider this side to be positive, and this side negative.

Â Current must flow in this direction, because of the direction of the diodes.

Â And V out is again positive, because current is flowing from its

Â positive terminal to its negative terminal.

Â The two output voltage equations from our previous analysis can be

Â combined into a single piece-wise linear equation,

Â that governs the behavior of our original circuit.

Â We can see that V out is equal to V in, when V in is greater than or

Â equal to 0, and V out is equal to minus V in, when V in is less than 0.

Â This is the state where D1 and D2 are on, and D3 and D4 are off.

Â This is the state where D1 and D2 are off, but D3 and D4 are on.

Â Now another way of writing this equation is,

Â V out is equal to the absolute value of V in, for any conditions.

Â And for this reason a full-wave rectifier,

Â is also known as an absolute value circuit.

Â Now let's ask the question how would the behavior of

Â the full-wave rectifier change, if we consider the diode to be non-ideal, or

Â we included its forward voltage drop, modeling it like this.

Â So here is the full-wave rectifier drawn, assuming the diodes to be non-ideal.

Â We're also going to assume that the input voltage is positive,

Â such that current flows, from the positive side of V in, around the loop,

Â through D1, through the resistor R.

Â Through D2 and back to the mono side of the battery.

Â So under those conditions we know that D1 and D2 are both on, and D3 and

Â D4 are both off.

Â So here I've redrawn the circuit, replacing D3 and D4 by open circuits, and

Â replacing D1 and

Â D2 by batteries of values Vf, to represent their forward voltage drop.

Â Now we know that in this circuit, the current must be flowing around the loop.

Â In this direction.

Â Now remember, that when a diode is on, the current through the diode must flow from

Â the positive side of Vf to the negative side of Vf,

Â because from the anode to the cathode of the diode, we must have a voltage drop.

Â Now here I've redrawn the circuit, to make it somewhat simpler, or more compact.

Â Here are the two Vf sources representing the for,

Â forward voltage drop across diodes D1 and D2.

Â Now we know for

Â this circuit to apply, the current must be flowing around the loop in this direction.

Â From the positive side of the Vf, to the negative side of Vf.

Â However, the polarity of the batteries Vf,

Â is attempting to push current around the loop in this direction.

Â So, in order for there to be a net flow of current in this direction, for

Â this circuit to apply, we know that the input voltage must be greater than 2Vf.

Â But we can write an equation to see that.

Â Let's write that,

Â V in minus Vf plus Vf, divided by R,

Â is equal to the current, in this direction.

Â We can see that, V in, minus 2Vf,

Â out over R, is equal to the current.

Â And for this current to be positive,

Â we can see that V in must be greater than 2 Vf.

Â So I positive, implies that V in,

Â is greater than 2Vf.

Â So the condition under which this circuit applies, I've drawn down here,

Â as V in is greater than 2Vf.

Â Now, we can also use this circuit to determine,

Â the output voltage in terms of the input voltage.

Â We can see that V in, I'm going to

Â write a loop equation around this loop, we go up by V in, we go down by V,out.

Â We go down by Vf, we go down by Vf.

Â Which implies that, V out for this circuit,

Â is equal to V in minus 2Vf.

Â Now, we can perform a similar analysis, assuming that D3 and D4 are on, and D1 and

Â D2 are off.

Â The resulting circuit, is drawn here.

Â Now, for this circuit to apply,

Â we know that current must flow around the loop in this direction.

Â From the positive side of Vf to the negative side of Vf.

Â However, the polarity of the batteries is such that,

Â they are attempting to push current around the loop in this direction.

Â So for there to be a net flow of current in this direction,

Â we can see that V in must be negative, with its positive side here and

Â its negative side here, and that its magnitude must be greater than, 2Vf.

Â So, I've written here the condition, under which this circuit applies.

Â Now we could, like we did for the last circuit, write an equation to

Â determine this, but let's just use this condition by inspection.

Â Now, we can use this circuit to determine the output versus input

Â voltage relationship like before, again by writing a loop equation.

Â So we go up by V in, we go up by V out, we go up by Vf,

Â we go up by Vf, as we go around the loop.

Â From this, we can see that V out, is equal to negative V in-

Â Minus 2Vf.

Â Now we can take the two results from these previous analyses and

Â put them into a single piece-wise linear equation, that describes the behavior,

Â of the full-wave rectifier.

Â So here we can see that the output is equal to V in minus 2Vf when V

Â in is greater than 2Vf.

Â And that V out is equal to minus V in minus 2Vf when V

Â in is less than minus 2Vf.

Â Now if the input voltage, is a voltage between these two voltages of 2Vf and

Â minus 2Vf volts, then we know that, none of the diodes are on.

Â The current through the resistor would be 0 and

Â the output voltage would be equal to 0.

Â So, our full-wave rectifier considering the diodes to be

Â non-ideal really has three states.

Â The case where D1 and D2 are on, the case where D3 and D4 are on, and

Â the case where none of the diodes are on.

Â Now I've plotted this equation here on this

Â graph assuming a sinusoidal input voltage.

Â The input voltage is in blue, the output voltage is in red.

Â And also on this graph I've labelled,

Â the threshold voltages of 2Vf, and minus 2Vf.

Â Now you can see that, when the input voltage is greater than 2Vf volts,

Â in this region here, that we obtain the output voltage by subtracting, 2Vf.

Â So we subtract a voltage of 2Vf,

Â from the input voltage to obtain the output voltage.

Â Then, when then input voltage is less than minus 2Vf, we obtain the output

Â voltage by multiplying this voltage by minus 1, and then subtracting 2Vf.

Â So in other words, we flip that about the x axis, and then subtract 2Vf.

Â And when we do that we obtain a shape exactly the same as we obtain,

Â when the input voltage is greater than 2Vf.

Â Now in the region where the input voltage is between the two threshold voltages of

Â 2Vf and minus 2Vf, we can see that the output voltage is 0.

Â So, let me leave you with some questions to think about.

Â If, in our full-wave rectifier circuit, the direction of

Â all four diodes was reversed, how would the behavior of the circuit change?

Â And, if you reversed the direction of any one of the diodes in the circuit,

Â how would the behavior of the circuit change?

Â So see if you can use our analysis, or

Â the methods we used during this lesson, to answer these questions.

Â So in summary, during this lesson,

Â we looked at the behavior of full-wave rectifiers.

Â And in our next lesson,

Â we're going to look what are called Voltage Transfer Characteristics, or

Â graphical depictions of the behavior of a nonlinear circuit.

Â Thank you and until next time.

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