# Diode Rectifier Circuits

We saw in the previous lecture that Zener diodes can be used in circuits that provide (1) voltage overload protection, and (2) voltage regulation.

An important application of “regular” diodes is in rectification circuits. These circuits are used to convert AC signals to DC in power supplies.

A block diagram of this process in a DC power supply is shown below

In this DC power supply, the first stage is a transformer:

An ideal transformer changes the amplitude of time varying voltages as

This occurs even though there is no direct contact between the input and output sections. This “magic” is described by Faraday’s law:

By varying the ratio N2/N1 in (1) we can increase or decrease the output voltage relative to the input voltage:
• If N2> N1 , have a step-up transformer
• If N2 For example, to convert wall AC at ~120 VRMS to DC at, say, 13.8 VDC, we need a step down transformer with a ratio of:

We choose s v1 ˜ V5DC for a margin. For the remaining stages in this DC power supply:
• Diode rectifier. Gives a “unipolar” voltage, but pulsating with time.
• Filter. Smoothes out the pulsation in the voltage.
• Regulator. Removes the ripple to produce a nearly pure DC voltage.
We will now concentrate on the rectification of the AC signal. We’ll cover filtering in the next lecture.

Diode Rectification
We will discuss three methods for diode rectification:
1. Half-cycle rectification.
2. Full-cycle rectification.
3. Bridge rectification. (This is probably the most widely used.)

Half-Cycle Rectification

We’ve actually already seen this circuit before in this class!

We will use the PWL model for the diode to construct the equivalent circuit for the rectifier:

From this circuit, the output voltage will be zero if Conversely, if vs(t ) >vds we can determine vO by superposition of the two sources (DC and AC) in the circuit sources since we have linearized the diode:

Notice that we’re not making a small AC signal assumption here. Rather, we have used the assumption of the PWL model to completely linearize this problem when ( ) 0 S D v t V > and then used superposition of the two sources, which just happen to be DC and AC sources. (Consequently, we should not use rd here.)
The total voltage is the sum of the DC and AC components:

In many applications,

A sketch of this last result is shown in the figure below.

There are two important device parameters that must be considered when selecting rectifier diodes:
1. Diode current carrying capacity.
2. Peak inverse voltage (PIV). This is the largest reverse voltage across the diode. The diode must be able to withstand this voltage without shifting into breakdown. For the half-cycle rectifier with a periodic waveform input having a zero average value
PIV = Vs
where Vs is the amplitude of vS.
Full-Cycle Rectification

One disadvantage of half-cycle rectification is that one half of the source waveform is not utilized. No power from the source will be converted to DC during these half cycles when the input waveform is negative.
The full-cycle rectifier, on the other hand, utilizes both the positive and negative portions of the input waveform. An example of a full-cycle rectifier circuit is:

Notice that the transformer has a center tap that is connected to ground.
On the positive half of the input cycle 0 S v > , which implies that D1 is “on” and D2 is “off.” Conversely, on the negative half of the input cycle, 0 S v < which implies that D1 is “off” and D2 is “on.”
In both cases, the output current i0(t ) >0 and the output voltage
V0(t)>0

While this full-cycle rectifier is a big improvement over the halfcycle, there are a couple of disadvantages:
1 PIV = 2Vs - VD), which is about twice that of the half-cycle rectifier. This fact may require expensive or hard-to-find diodes.
1 Requires twice as many transformer windings on the secondary as does the half-cycle rectifier.

Bridge Rectification

The bridge rectifier uses four diodes connected in the famous bridge pattern:

Oftentimes these diodes can be purchased as a single, fourterminal device.
Note that the bridge rectifier does not require a center-tapped transformer, but uses four diodes instead.
The operation of the bridge rectifier can be summarized as:
1. When
are “off”:

2. 3. When
4. are “on”:

The bridge rectifier is the most popular rectifier circuit. Advantages include:
1 PIV = Vs - VD), which is approximately the same as the half-cycle rectifier.
2 No center tapped transformer is required, as with the half cycle rectifier.