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

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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.

Â This is Dr.Robinson.

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

Â In previous lessons, you looked at analyzing circuits containing resistors,

Â diodes and dc sources.

Â And in the process of doing this, you modeled the diodes both as ideal and

Â as non-ideal, considering the forward voltage drop that exist across the diodes.

Â Our objectives for

Â the lesson are to introduce what are call half-wave rectifiers.

Â Well then examine their behavior for sinusoidal inputs and

Â then analyze a particular diode circuit that implements a half-wave rectifier.

Â So here's the definition of the rectifier.

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 value.

Â Now let me illustrate this definition with a picture.

Â So here I've represented the half-way rectifier as a block,

Â and later on in the lesson we'll look at the circuit that is actually inside this

Â block to implement it.

Â For the input to this block, I've applied a sinusoidal varying voltage.

Â This is the zero volt level.

Â So for each half-period, the voltage is positive and for

Â the second half-period, the voltage is negative.

Â Now when we apply this sinusoidal voltage to this half-wave rectifier,

Â from the definition I gave you from the previous slide,

Â there are a number of possible outputs.

Â Let's look at this possible output first.

Â You can see that to obtain the output voltage from the input voltage in this

Â case, when the input voltage is a positive value or greater than the zero-volt

Â threshold, then the output voltages is exactly equal to the input voltage.

Â But, when the input voltage is negative or

Â less than zero volts, the output voltage is set equal to zero volts.

Â Now, this wave form is known as a positive half-wave rectified sine wave.

Â Positive, because it's entirely greater than zero volts, or

Â greater than the zero-volt threshold.

Â And so, it's the half wave rectified sine wave because the output is

Â non-zero only for each half-period of the input waveform.

Â Now, the waveform I've drawn down here is known as the negative half-wave

Â rectified sine wave.

Â Half-wave rectified, again, because the output is non-zero only for

Â every half-period of the input.

Â And negative because it's entirely below the zero-volt threshold.

Â So in this slide I have represented a positive half-wave rectifier in terms of

Â rules that are applied to the input to obtain the output.

Â The input is applied.

Â If the input is greater than the threshold,

Â then the output is equal to the input.

Â But if the input is less than or

Â equal to the threshold, the output is equal to the threshold.

Â Let's look at a circuit that can be used to implement a half-wave rectifier.

Â Now you've seen circuits similar to this one in previous lessons in this course.

Â The circuit consists of an input voltage and series with resister and

Â series with ideal diode.

Â And I have defined this node here as the ground node, or

Â the zero-volt reference node.

Â Now remember, an ideal diode can be thought of as a voltage-controlled switch.

Â When this voltage at the anode is greater than the voltage at the cathode,

Â the diode is forward-biased, or said to be on,

Â and can be thought of as a closed switch or a short circuit.

Â However if the voltage here at the cathode is greater then the voltage at the anode,

Â the diode is set to be reversed biased or off, and

Â can be thought of as an open switch or an open circuit.

Â So in the case where V-in is a positive voltage,

Â that means that V-in is attempting to push current around the loop

Â in this direction from its positive terminal to its negative terminal.

Â However, the direction of the diode does not allow current to flow in

Â that direction.

Â Remember current can only flow from the anode to the cathode of the diode when

Â it's forward biased.

Â So when V-in is positive, current should flow in this direction.

Â However, it's prevented by the diode, the voltage of the cathode

Â is greater than the voltage of the anode, the diode is reversed biased, or off.

Â And we can model this circuit as I've drawn here,

Â with the diode replaced by an open circuit.

Â Now, in this case where V-in is negative, remember if V-in is negative we can think

Â of this side as the positive side, and this side as the negative side.

Â So with V-in negative it's attempting to push current around the loop in

Â this direction.

Â That direction is allowed by the direction of the diode.

Â This voltage is more positive than this voltage.

Â The diode is on and it can be replaced by a short circuit as I've drawn here.

Â So these two circuits in combination model the behavior of your original circuit.

Â This one applies when V-in is negative, this one applies when V-in is positive.

Â On this slide I've redrawn the two circuits.

Â Now, it may be apparent to you the relationship between the output and

Â input voltages for each of these two circuits.

Â But let's go ahead and

Â write some equations to determine those relationships.

Â Because thinking about circuits in this way will help you to analyze more

Â complicated circuits.

Â Now, in this circuit you can see that the output voltage is the voltage

Â between this node and this node.

Â So to get from this node to this node, I go up by a voltage V-in,

Â then I go down by 1IR drop by ohm's law across the resistor.

Â So, we can write that V-out is equal to, we go up from V-in, and

Â then we go down by an IR drop across the resistor to get to V-out.

Â But we know, because of the open circuit, that I is equal to 0,

Â which implies that V-out is exactly equal to V-in.

Â Now, in the second circuit we can see immediately that the out voltage is

Â the voltage measured across a wire, or a resistor of 0 ohm's.

Â Well let's go ahead and write the equation.

Â V-out is equal to I times the resistance of a wire,

Â is equal to V-in divided by R, the current times R wire.

Â But we know that the resistance of a wire, is equal to 0.

Â Which implies that that V-out is equal to 0, for this case.

Â Now remember, these two circuits in combination model the behavior of our

Â original circuit.

Â So I can take these two circuits and form a single piecewise

Â linear equation that represents the behavior of the original circuit.

Â Here I've combined the results of the previous slide into a single piecewise

Â linear equation that describes the behavior of the circuit.

Â The output voltage is equal to the input voltage when V-in greater than 0.

Â The output voltage is equal to 0 when V-in is less than or equal to 0.

Â Now if we apply this sinusoidal input voltage to that circuit,

Â we can determine the output voltage of the circuit by using these rules.

Â For the case where V-in is positive,

Â we can see that the output is exactly equal to the input.

Â So I just copy the input to the output graph when V-in is positive.

Â But when V-in is less than 0, we can see that the output is equal to 0.

Â So from this graph we can see that that circuit that we've analyzed

Â implements a positive half-wave rectifier.

Â Now up to now we assume the diodes were ideal.

Â But what happens if we include the forward voltage drop that exists across a diode

Â when it's turned on?

Â In other words, we model the diode in the original circuit by this circuit here,

Â a battery of Vf, the forward voltage drop in series with an ideal diode.

Â So here I've redrawn the circuit to include the forward voltage drop model.

Â The voltage here is 0 volts, or ground, by definition.

Â To move from this voltage to this voltage,

Â we go down by one voltage drop of Vf volts.

Â Because remember in the battery symbol, the longer side is the more positive side.

Â So 0 minus Vf gets us to this node voltage.

Â So we can label the node voltage here as -Vf volts.

Â Now we can analyze the circuit,

Â just considering the behavior of the ideal diode.

Â Say V-in is a positive voltage such that V-in is greater than minus Vf volts.

Â Then we know the voltage here is greater than the voltage here, which means

Â the diode is off, or reversed-biased, and can be replaced by an open circuit.

Â So, under the condition where V-in is greater than -Vf volts,

Â we redraw the circuit like this.

Â Now for the condition where V-in is less than minus Vf volts,

Â the voltage of the anode would be greater than the voltage of the cathode.

Â The diode would be on and we can represent it as a short circuit.

Â So I've redrawn the circuit here under those conditions,

Â where the output voltage is taken directly across the battery Vf.

Â So lets just analyze the relationship between the output voltage and

Â the input voltage by inspection, rather than writing equations.

Â We can see that in this case the output voltage is exactly equal to

Â the input voltage for the same reasons as it was for the ideal diode case.

Â V-out is the voltage between this node and this node.

Â We go up by V-in and down by one IR drop, but i is equal to 0.

Â Now in this case, we can see that the V-out is the voltage taken directly

Â across a battery of the Vf volts.

Â However the polarities are different.

Â V-out is defined positive on this side but Vf is defined as positive on this side.

Â So we can write that for this case, Vf is equal to -Vf volts.

Â We then combined the two results into a single equation in V-out.

Â In this equation we can see that V-out is equal to V-in when

Â V-in is greater than -Vf volts.

Â And that V-out is equal to minus Vf when V-in is less than or equal to -Vf volts.

Â Now rather than plotting this equation I went to the lab and built on a proto board

Â the circuit we've been analyzing using a one-end 4148 small signal silicon diode.

Â I applied a sine wave to the input and

Â used an oscilloscope to measure the output voltage and input voltage of the circuit.

Â Here's the oscilloscope trace.

Â You can see the input voltage here.

Â This sign is subtly varying voltage.

Â Let me label on this graph -Vf volts, which you may remember for

Â a silicone diode is approximately 0.65 volts.

Â So this is a 2-volt by 200 microseconds squared.

Â So minus 0.65 would be

Â Right there.

Â So we can see that when the input is greater than -0.65 volts,

Â the output is equal to the input and the two curves track each other exactly.

Â But when the input voltage is less than our -0.65 volt level,

Â the output is equal to -0.65 volts, as we would expect from our previous analysis.

Â The circuit we've been analyzing has this particular typology.

Â An input voltage in series with element 1 in series with element 2.

Â Now if we had available to us one resistor and one diode, we can build four different

Â rectifier circuits, assuming that the output voltage is taken across element 2.

Â Now I wanted to leave you with some things to think about at the end of this lesson.

Â For each of these possible circuits,

Â can you perform the same analysis that we did during this lesson?

Â In other words,

Â can you determine the output voltage verses input voltage equation?

Â And additionally, say we took the output across element 1 rather than element 2.

Â How would the output voltage change for each circuit?

Â So in summary, during this lesson we looked at rectification and

Â we looked at a particular type of rectifier known as a half-wave rectifier.

Â In our next lesson we'll look at circuits known as full-wave rectifiers, and

Â determine how they differ from half-wave rectifiers.

Â Thank you and until next time.

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