Electronics Module 4B: Diode Circuits
In the last Module we introduced a new circuit component, the diode. At its simplest, a diode is a device
which carries current in only one direction, and its schematic symbol – an arrow – is strongly suggestive
of this function. The impetus for the diode’s development was the need for “detection” of radio signals,
and conversion of AC to DC. Both of processes require rectification (the conversion of 2-way current
flow into 1-way), and thus a device which could differentiate between current flowing in one direction,
and current flowing in the other. Since then, many more applications for diodes have been developed.
In this Module we will discuss some practical diode-based circuits: the rectifier, the detector, the
voltage multiplier, the clipper and the clamper. We will finish by discussing some specialty diodes
which have a diverse array of applications in electronics; foremost among these are the Zener diode, the
Schottky diode and the light-emitting diode (LED), although there are others. The Zener diode is widely
used in voltage regulators and transient suppressors, while LEDs find heavy use in a number of
applications; indeed, LEDs are beginning to replace the trusty old incandescent light bulb in many cases.
Schottky and other diodes are typically used at very high frequencies, where the effects of junction
capacitance and recovery time start to become significant.
0.
Review so far
Though early diodes typically were based on vacuum tubes and depended on thermionic emission from
a cathode to an anode (sometimes called a plate), or lightly-touching (and unreliable) metalsemiconductor contacts such as the “cat’s whisker,” almost all modern diodes are based on
semiconductor junctions. Understanding such “junction diodes” or “semiconductor diodes” required us
to delve into some solid-state physics; this is why such devices, which operate because of intrinsic
properties of bulk materials, as opposed to vacuum tubes, are often referred to as “solid-state devices”).
We learned that in real materials (which are somewhat more complicated than the simple picture of the
Drude model we used to “derive” Ohm’s law), electrons will tend to occupy the lowest-available energy
states up to the so-called Fermi level. These available energy states are grouped into “bands” with
forbidden gaps between them due to the interaction of electrons (which have a de Broglie wavelength 
= h/p due to wave-particle duality) with the periodic atomic lattice. While metals have their Fermi level
in the middle of an allowed band and thus have an abundance of mobile carriers, and insulators have
their Fermi level located in the midst of a very large energy gap and thus have very few mobile carriers
at typical temperatures (since there is insufficient thermal energy to excite free carriers across the band
gap), semiconductors have their Fermi level located inside a narrower energy gap, so there are a
moderate number of available carriers at typical temperatures. For this reason, semiconductors
typically have a somewhat higher resistivity than metals, but significantly lower than most insulators,
but like insulators have a negative temperature dependence of resistivity: as temperature increases,
resistivity decreases, since the number of available carriers increases with rising temperature.
While intrinsic semiconductors, like metals, typically exhibit behavior that fits quite well with Ohm’s
Law, if we join together two pieces of semiconducting material which have been doped – one with
impurities that reduce the total number of electrons (p-type), and one with impurities that increase the
total number of electrons (n-type) – the behavior is totally different. Since the band energies are shifted
somewhat in the p-type and n-type materials, mobile carriers (electrons and holes) will tend to travel to
opposite sides of the junction in order to minimize the total energy. This leads to a so-called ‘depletion
region’ around the junction in which there is a paucity of available carriers, so the material’s ability to
conduct electricity is strongly suppressed.
When a voltage is applied across the junction in a direction which tends to amplify this charge imbalance
(reverse bias), the depletion region in enlarged, and current cannot flow. But when a voltage is applied
in a direction which tends to remove this charge imbalance, the depletion region eventually disappears,
and current readily flows.
To deal with the practical electronic characteristics of diodes, we introduced the I-V plot, which depicts
the current conducted (on the vertical axis) versus the applied voltage. Our ideal conductor, ideal
insulator and ideal resistor have a linear relationship on the I-V curve, with an intercept of zero (zero
drawn current for zero applied voltage) and a slope equal to 1/R (with R = 0 corresponding to an ideal
conductor, and R   corresponding to an ideal insulator). Diodes have a nonlinear I-V characteristic,
and to deal with them, we introduced three models of diode behavior.
First we introduced the “ideal diode model,” in which a diode behaves as an ideal insulator for V < 0
(reverse bias, so zero current flows no matter how much reverse-bias voltage is applied) and an ideal
conductor for V = 0 (i.e. zero voltage drop across the diode for any quantity of forward current).
Though the ideal diode model is good enough for a number of tasks, we found that it does not exactly
describe the way a diode behaves, so we had to develop two more complex models.
We noted that the ideal diode model failed to account for (a) the small amount of current conducted
even while the diode was in reverse bias (typically on the order of A), (b) the fact that a large enough
reverse-bias voltage (greater than the peak inverse voltage, PIV, or peak reverse voltage, PRV, typically
hundreds of volts or larger) will cause the diode to break down and conduct, (c) the fact that the
depletion zone does not disappear immediately, so that the current increases gradually with increasing
forward voltage, and (d) the fact that even once the depletion zone is suppressed, the semiconducting
material still has some bulk resistivity that causes it to behave like a resistor with a finite resistance (on
the order of tens of ohms).
Consideration of all of these led us to the Shockley model of diode behavior, which describes an
exponentially-increasing current as a function of forward voltage, and to the so-called “complete diode
model,” which is described by a rather complicated I-V characteristic curve. The only major issues our
complete diode model do not address are the small (typically ~100 pF) capacitance that exists in the
vicinity of the junction, and the finite time required for the depletion region to generate and dissipate;
the effects of this junction capacitance and time required for the depletion region to expand or contract
become increasingly bad as frequency increases. So at high frequencies we must take special care to
account for these problems, or use specialized diodes (such as the Schottky diode) which reduce them.
That said, while the complete diode model does an excellent job describing exactly how a diode behaves
under most circumstances, it’s rather difficult to work with for circuit analysis, resulting in
transcendental equations that require numerical or graphical solution. So we also developed a
“practical diode model,” in which the exponentially-increasing current as a function of forward voltage is
replaced by a sudden “turn-on” when the forward voltage reaches a threshold value VD. The value of VD
is an approximation to the Shockley model, and is a function of temperature and the material the diode
is made out of. For silicon diodes (the most common type), VD ~ 0.7 V, and for germanium, VD ~ 0.3 V.
However, as long as our applied voltages are never extremely close to VD (so a diode is always either “all
on” or “all off”), reverse biases on the order of the PIV are never reached, the forward currents are
significantly larger than the reverse leakage currents, and the external resistances in the circuit are
significantly larger than the diodes’ internal resistances – and for the majority of circuits these are
generally true - for all intents and purposes the three diode models yield very similar predictions.
So, for basic circuit analysis we will generally use the ideal diode model, applying the practical diode
model when we wish to improve upon our results, and relying on the much more difficult-to-apply
complete diode model only when necessary.
I.
Rectification
If there is a “killer app” for diodes, it’s in rectification, the conversion of AC power (which could be
transported over large distances with minimal losses thanks to transformers) into DC power for use in
appliances and devices.
A. Half-Wave Rectifier
The simplest rectifier, which uses a single diode, is known as the half-wave rectifier. In the half-wave
rectifier, during the “positive” half of the cycle (current flows clockwise from the source), the diode D is
in forward bias. Thus D drops a voltage VD (typically around 0.3-0.7 V), and passes the remainder on to
the load. During the “negative” half of the cycle, the diode is in reverse bias, so a very small current
flows (typically A or smaller, which is usually thousands of times smaller than what flows during the
forward-biased half of the cycle, so it is negligible), and the output voltage is zero. The output is a
voltage which fluctuates in time, but which is always positive.
Left: Half-wave rectifier circuit. Center: Input AC voltage. Right: Output “rectified AC” voltage, which
comes from the positive half of the cycle (with a peak value equal to Vin_peak – VD). During the negative
half of the cycle, no current flows and hence Vout = 0.
If the peak voltage going in to a half-wave rectifier is given by Vin_p, we know that its average voltage is
Vin_avg = (2/)Vin_p. The peak output voltage coming out is given by
Vout_p = Vin_p – VD
where VD is the forward-bias voltage drop across the diode (~0.7V for silicon diodes, for example). The
minimum output voltage will of course be zero (or nearly so). The average voltage coming out is
Vout_avg = (1/) (Vin_p) – VD = (1/2)Vin_avg – VD
That is, the average value of Vout is half of the average value of Vin, diminished by the voltage VD dropped
across the diode. If Vin >> VD (which is often the case), we can assume VD = 0, and apply the “ideal diode”
model, in which case Vout = Vin/2.
The half-wave rectifier as it stands is quite wasteful, since you are “throwing away” half of the cycle. So
let’s think of more efficient rectification circuits.
B. Full-Wave Rectifier
The next type of rectifier we will consider is the full-wave rectifier.
Left: Full-wave rectifier circuit. The center-tapped transformer is necessary in order to have access to
the “zero voltage;” current flow during the positive half-cycle is indicated by red, and current flow during
the negative half-cycle is indicated by blue. Center: Input voltage Vin(t). Right: Output voltage; during
each half-cycle either the “blue” or the “red” flow pertains, so Vin/2 (minus VD) is passed along to the
output, with positive polarity during either cycle due to the orientation of the diodes.
In order to use this rectifier, we must have access to the “zero” voltage, that is, a voltage exactly in
between that of the two end terminals. The most straightforward way to do this is to take our output
across a transformer with a center tap; even if we do not wish to transform the input voltage we can use
a 1:1 transformer (sometimes known as an “isolation transformer” since it electrically isolates the input
side from the output side). Then each “half” of the outbound leg of the transformer is fed into a halfwave rectifier of opposing polarity.
During the positive half of the cycle, the upper diode is in forward bias, so the upward half of the
transformer conducts a current depicted by the red arrows. During the negative half of the cycle, the
bottom half of the transformer conducts a current through the lower diode, which is now in forward
bias, with current traveling as depicted by the blue arrows. Because of how the circuit is connected,
during both cycles the polarity of the output is the same. However, because the output is coming from
only half of the transformer at any time, the output voltage is reduced by half: if the peak input voltage
is Vin_p and we are using a 1:1 transformer, the peak output voltage is
Vout_p = Vin_p/2 – VD
(due to the single diode in forward bias over each half of the cycle). Since the average input voltage is
Vin_avg = (2/)Vin_p
it follows that the average output voltage is
Vout_avg = (2/) (Vin_p/2) – VD = (1/2)Vin_avg - VD
Therefore, while the full-wave rectifier conducts over the entire cycle, it doesn’t deliver any more power
to the load than the half-wave rectifier, since you’re only using half of the input voltage at any given
time. However, the full-wave rectifier delivers a smoother, more uniform output since it’s not
alternating between “everything” and “zero,” but rather between one half of the output side of the
transformer, and the other half of the transformer output.
And again, in the limit that Vin >> VD, we can take VD = 0, in which case Vout = Vin/2.
C.
Bridge Rectifier
However, there is another rectifier, which uses four diodes, which uses all of the voltage, all of the time,
to maximize conversion efficiency. This is known as a full-wave bridge rectifier, or bridge rectifier,
pictured below.
In the bridge rectifier (so named because of its resemblance to the Wheatstone bridge we studied
earlier), two of the diodes are forward-biased during the positive half of the cycle (red arrows, left
picture), and the other two are forward-biased during the negative half of the cycle (blue arrows, center
picture). The output voltage is as seen in the right panel: it is similar to that of the full-wave rectifier,
but without a reduction factor of two.
Left: Bridge rectifier circuit; current flow during positive half-cycle. Center: Current flow during negative
half cycle. Right: Output voltage; during each half cycle a voltage Vin(t) – 2VD is passed to the output,
with the same polarity over the whole cycle due to the orientation of the diodes.
If the input peak voltage is Vin_p, and the input average voltage is Vin_avg = (2/)Vin_p, the peak output
voltage is given by
Vout_p = Vin_p – 2VD
since there are two diodes in forward bias on each half of the cycle. The average output voltage is then
Vout_avg = (2/) Vout_p = (2/) (Vin_p – 2VD) = Vin_avg – (4/) VD
Again, in the limit Vin >> VD, we can take VD  0, so Vout = Vin, and in principle the output DC voltage can
have an amplitude quite close to the peak input voltage.
For this reason, the bridge rectifier is the most efficient of the three rectifiers studied here, and is
probably the most widely-used.
D. Filters
You may be scratching your head at this point and wondering whether I pulled a fast one. What we’re
getting out of these rectifiers is not DC as we know and love it: a constant voltage which does not vary
with time. What we’re getting instead is a voltage (and current) whose sign remains the same, but
whose value varies between zero and a maximum value. This is usually known as “rectified AC.”
Well, how to we get good old, honest-to-God DC out of these circuits? This brings us back to our old
friend, the capacitor. If we connect the output of our rectifier across a rather large capacitor, the
capacitor will tend to “smooth out” (or “condense,” hence the old name for capacitors: condensers) the
fluctuations. That is, the capacitor acts as a “low pass filter,” filtering out the high-frequency (quickly
fluctuating) component to the voltage, leaving behind only a smooth oscillation known as a “ripple
voltage,” which can hopefully be made negligibly small.
To keep things simple, let’s consider a half-wave rectifier (whose output is Vout) connected to a filter
capacitor C; the load is connected across the capacitor and is subjected to a voltage Vfilt = VC.
Left: Half-wave rectifier / filter combination. Center: output of rectifier if the capacitor C is absent; this
is the same as in the half-wave rectifier figure given previously. Right: output of rectifier with C present;
instead of the voltage oscillating between 0 and Vout_max = Vin_max – VD, it acts more like a DC voltage with
VDC approaching Vin_max – VD, and a small “ripple” voltage superimposed. As C becomes larger,  = Rload C
increases and hence Vripple decreases.
Another equally valid way to think about this circuit, which leads us to more quantitative conclusions, is
to consider the “filter” portion to be an RC circuit (remember, our old friends with the time constants!):
During the times that Vout (of the rectifier) is increasing, we can consider the capacitor C to be
“charging,” with a time constant given by
C = Rrect C
where Rrect represents the effective resistance of the rectifier portion of the circuit (i.e. everything to the
left of the capacitor). Rrect is manifestly quite small (on the order of ohms, since it comes from only the
diode), and therefore the capacitor charges rather quickly (ideally, the capacitor voltage will closely
“follow” the input voltage Vin(t) as it increases, in the limit that C << 1/f).
When Vout begins decreasing, however, C begins to discharge into the load. The time constant of this
“discharging” circuit, and hence the diminution of VC = Vfilt, is given by
D = Rload C
where Rload is the load resistance. Generally, Rload will be significantly larger than Rrect, so D >> C. In
particular, we want D >> T = 1/f, so that the capacitor only partially discharges between one Vout pulse
and the next. If this is the case, then Vfilt does not drop significantly between pulses, and the “ripple
voltage” Vripple is small. In the limit that Vripple  0, we get back a very nice DC signal.
Note that Vripple is primarily a function of C, Rload and f.
All else being equal, the larger the value of C, the larger the “discharging” time constant D, and the
smaller Vripple will be. However, the size of C is limited both by practical factors (the largest C you can
find that’s capable of handling voltages up to Vout_p) and by the fact that a very large “surge current” may
flow as the large capacitor C charges; all your devices (source, wiring, diode(s) and capacitor) must be
rated to handle this large “surge current.”
The half-wave rectifier and filter combination places a very “asymmetric” load on the source – very large
currents are drawn from the source during the “charging” cycle, and zero current is drawn during the
“discharging” cycle. In the full-wave rectifier, the load is also asymmetric – though only moderately
large currents are drawn over the entire cycle, the load is drawn from only half of the transformer (i.e.
the “upper half” or the “lower half” during each half-cycle, with the “loaded half” alternating back and
forth. The bridge rectifier, though, places a rather uniform load on the source as a function of time;
again, this is why the bridge rectifier is generally superior to the two simpler versions.
Put another way, the frequency f ( = 1/T = /2) of the AC source tells us how much time elapses
between successive “pulses” of rectified AC coming out of the rectifier. The lower the frequency, the
longer we need D to be in order to keep Vripple small. But a half-wave rectifier is “harder” to de-ripple
than a full-wave or bridge rectifier, since there is a longer “gap” (the full T, rather than T/2) between
successive pulses. And this is the chief advantage of the full-wave and bridge rectifiers, although the
bridge has the added advantage of giving you the “full” Vin, without asymmetric loading of the
transformer.
In addition, the smaller the value of Rload, the shorter the discharging time constant D will be
(heuristically, a smaller load resistance pulls more current off of the capacitor, which discharges it more
quickly). Therefore, C must be “sized” to accommodate the minimum load resistance you anticipate
connecting to the circuit (or must be adjustable so you can adapt to larger current-drawing loads).
Finally, there will always be some ripple voltage left. Even if we use the maximum practicable value of
C, there will still be some ripple, if the frequency is low enough, or the load draws enough current. To
get rid of this residual ripple, we will have to use a voltage regulator, which we’ll come back to in just a
little while, when we talk about clippers, and Zener diodes.
II.
Detectors: The Diode’s Original Raison d’Etre
If there is one thing that diodes were historically developed for, it is detection. A detector is a circuit
which takes a radio-frequency signal, drawn from the airwaves with an antenna, and converts it into a
form which is suitable for output to a speaker.
An amplitude-modulated (AM) radio signal is an AC voltage oscillating at a frequency on the order of
MHz (or even GHz); information is encoded in the signal by modulating the amplitude of the RF “carrier”
as a function of time. The corresponding audio signal (which has a frequency of hundreds of Hz to kHz,
so on time periods thousands of times longer than the RF oscillation) is effectively “superimposed” on
top of the RF signal. Detecting the signal involves finding a way to remove the RF oscillations, leaving
behind only the low-frequency audio oscillations; the most straightforward way to do this is to use a
diode to eliminate one half (say, the negative half) of the signal, and then passing the signal across a
capacitor to “filter out” the high-frequency oscillations.
In a practical radio circuit, the signal is picked up using an antenna (which, as we learned, is merely a
resonant RLC circuit at the frequency of interest). The RF frequency of interest is singled out with much
higher selectivity using a high-Q LC circuit whose resonant frequency can be tuned (e.g. with a variable
capacitor). Once the RF frequency of interest is isolated through tuning of the LC circuit, it is passed
through a diode (to clip the negative portions), and then across a capacitor (to filter out the highfrequency oscillations), leaving behind only the audio-frequency signal which can be passed to a
speaker. Of course, more modern radios use active signal processing and have multiple amplifier and
mixer states to produce a much higher-quality signal, but a basic radio of this sort does in fact work!
Historically, “cat’s whiskers” were first used for the diode stage, but were extremely finicky and
unreliable. That is why the development of the vacuum tube diode was such a great achievement, as it
made it possible to reproducibly construct radio circuits which would operate reliably over lengths of
time. Nowadays, semiconductor diodes are used instead, but the principle of operation is the same.
Above: a schematic diagram for an extremely simple radio circuit. RF signals are picked up by the
antenna. The parallel LC circuit is used to “tune” the frequency of interest, the diode is used as the
“detector,” which is really just a half-wave rectifier, and the capacitor/resistor is used to filter out the
high-frequency RF signal to leave behind the audio signal, which is sent along to the earphone (an
earphone is necessary since there is not enough power to drive a speaker: there is no power source in this
circuit, so the energy to produce the sound is actually coming from the air!) Courtesy
http://www.techlib.com/electronics/crystal.html
Above left: Incoming RF signal (rapid oscillations) with audio signal (slower oscillations) superimposed as
the time-varying intensity of the signal. Center: remaining signal after passing through a diode (as a
half-wave rectifier), which clips off the negative portions. Right: Signal after being passed across a
capacitor (low-pass filter); the high-frequency oscillations are averaged over (although a small ripple
may remain), leaving behind only the audio signal of interest.
III.
Voltage Multipliers
Now that we’ve explored the diode’s “killer apps” in rectification and detection, we’ll move on to some
of the diode’s other uses.
One particularly useful application of the diode, going beyond the simple conversion of AC into DC, is
the conversion of AC into a DC voltage whose amplitude is higher than the input AC voltage. While ACto-AC conversion is readily accomplished using a transformer, such voltage multipliers (which can also
be used to transform DC voltages through the use of rapid switching (i.e. using a switch to periodically
reverse the polarity of an input DC voltage) have in recent years come into heavy usage.
Consider the circuit below, which is a full-wave voltage doubler.
During the positive half-cycle (current moves upward through the source), note that diode D1 is in
forward bias, while D2 is in reverse bias. Therefore, current flows through C1, and charges it up to
voltage V0 (in the limit that the diode voltage is negligible) during the ascending half of the cycle.
During the negative half-cycle (current moves downward through the source), diode D1 is in reverse
bias, and D2 is in forward bias. Therefore, current flows through D2 and charges capacitor C2 during the
ascending (in magnitude) half of the negative half-cycle.
In the limit that the discharging time constants (i.e. the time taken for C1 and C2 to discharge through C3
and the load) are longer than the time spent on the descending portions of the input voltage cycles,
capacitor C1 eventually charges up to a steady-state voltage VC1 = V0, and capacitor C2 eventually charges
up to a voltage VC2 = V0 as well.
We may equivalently think of the two “halves” of the circuit (the “upper” half containing C1 and D1, and
the “lower” half containing C2 and D2) as half-wave rectifiers/filters with opposite polarity. That is,
provided that the capacitors are large enough to minimize the ripple voltage, the C1/D1 combination
produces a rectified VDC = Va-Vb = V0 output from the positive half-cycles, and the C2/D2 combination
produces a rectified VDC = Vb-Vc = V0 output from the negative half-cycles.
Note that both C1 and C2 have their top terminals positively charged, and their bottom terminals
negatively charged. That is, if we treat the bottom terminal of the source as being grounded to V = 0,
Va = +V0, Vb = 0, and Vc = -V0.
Since capacitors C1 and C2 discharge through C3 (which itself is connected between nodes a and c),
eventually C3 charges up to
VC3 = VC1 + VC2 = (Va-Vb) + (Vb-Vc) = Va - Vc = 2V0
The output voltage of this circuit Vout (= VC3) is thus equal to 2V0 (again, in the limit that the diode
voltage drops are negligible).
There are many other circuits which will multiply voltages. The simplest is the Cockcroft-Walton voltage
multiplier (forms of which are depicted below), in which the capacitors charge during alternate halfcycles and the output is taken across several capacitors effectively in series; for this reason the C-W
voltage multiplier is also referred to as a half-wave voltage multiplier.
For convenience, one can imagine the sinusoidal source being replaced by a square-wave source (or a
DC source whose polarity is periodically reversed). In fact, this is also one of the great advantages of
diode-based voltage multipliers: while transformers will only cleanly amplify sinusoidally oscillating
voltages, diode-based voltage multipliers will multiply any waveform – sinusoidal, triangular or square –
and produce a DC output whose ripple is negligible as long as the filter capacitors are sufficiently large.
By stacking together multiple stages of voltage multipliers, one can produce voltage triplers, voltage
quadruplers, and in fact any multiple of the input voltage. In such devices, each capacitor typically
charges over successive half-cycles to the peak input voltage Vin; since the output is taken across a series
combination of N of these capacitors, the output voltage Vout = NVin.
Left: voltage tripler. Right: voltage quadrupler. Courtesy http://www.coolcircuit.com.
IV.
Clippers
In addition to voltage rectification and multiplication, diodes can also be used for shaping (or “clipping”)
time-varying voltages.
The simple half-wave rectifier we studied earlier is also a simple example of a clipper (known as a series
clipper since the diode is in series with the load) as it “clips” any voltage V < 0, although it allows all V > 0
to pass (albeit diminished by an amount VD). If we reverse the direction of the diode (to produce a
“negative half-wave rectifier”) we also have a clipper, one which clips all V > 0, while passing all V < 0.
However, practical clippers are generally designed with the diode connected “across” the source, so that
it is effectively in parallel with the load, “shunting away” any voltages in excess of what you would like
to pass. For this reason, such clippers are known as shunt clippers.
The shunt clipper is pictured below. Whenever Vin(t) < 0 (current goes downward through the source),
the diode is in forward bias. Hence VD = 0 (or some nominally small amount, so the diode effectively
acts as a short), and since the load is connected in parallel with the diode, Vout = 0. (It follows that the
entire source voltage is dropped across the “shunt resistor” Ri.) However, when Vin(t) > 0, the diode is in
reverse bias and acts as an “open circuit,” so the voltage is passed directly to the load. That is, after
some amount is dropped across the shunt resistor Ri; this circuit acts like a classic voltage divider.
Therefore,
Vout
=
=
Vin(t) * RL / (Ri+RL)
0
for Vin(t) > 0
for Vin(t) < 0
That is, only the “negative” voltages of the input cycle are passed to the output, with all positive
voltages “clipped” to zero.
If the polarity of the diode were reversed, then the negative halves of the Vin(t) cycles would be passed,
and the positive cycles would be “clipped” to zero.
Upper panels: Diode clipper circuit, assuming the
ideal diode model, so VD = 0 in forward bias. When
Vin(t) > 0, the diode is in reverse bias, so the diode leg
appears as an open circuit, and Vout(t) = Vin(t) in the
limit that the load resistance RL >> Ri.
Lower panels: Diode clipper circuit with diode
reversed. If Vin(t) > 0, the diode is in forward bias, and
shorts the output. If Vin(t) < 0, the diode is in reverse
bias and the diode leg appears as an open circuit.
Now, what if we want to clip voltages at some value other than zero? To do that, we add a bias voltage
VDC in series with the shunt diode.
In the circuit below, whenever Vin(t) < VDC, the diode is in forward bias and acts as a short, so Vout = -VDC
(again, in the limit that VD =0 in forward bias). However, whenever Vin(t) > -VDC, the diode is in reverse
bias, and the circuit once again acts like a voltage divider, so
Vout
=
=
Vin(t)*RL / (Ri+RL)
-VDC
for Vin(t) > -VDC
for Vin(t) < -VDC
Above: Biased diode clipper circuit. The diode is forward-biased for any Vin(t) < -VDC, and shorts any such
voltage, so that the output voltage Vout = -VDC. For all Vin(t) > VDC, the diode is in reverse bias, and Vout(t) =
Vin(t) in the limit that the load resistance >> Ri (otherwise the circuit acts as a voltage divider).
If I were to reverse the polarity of the DC bias source, -VB would be replaced with +VB (i.e. I could clip the
output to a positive minimum voltage).
If I were to reverse the polarity of the diode, the circuit would clip voltages falling above -VDC (i.e. -VDC
would become a maximum passable voltage, rather than a minimum).
Finally, we may ask why Ri is present. It seems to complicate matters, as the output voltage fails to
follow the input voltage exactly in the non-clipped regime. It is, however, necessary, as in the “clipped”
regime the diode is in forward bias and acts as a short. That is, the source is effectively shorted
whenever the voltage falls outside the clipper’s range. Ri, therefore, acts as a current-limiting (and an
excess voltage-dropping) resistor, and protects the source, diode and wiring against excessive currents.
In the limit that Ri << RL (depicted in the figures), its effect on the output voltage is minimal.
Therefore, one would ideally set RS to the minimum feasible value, where the limit comes from the
maximum current and power ratings on the power supply, the diode, the DC bias source, and the wiring.
V.
The Clipper as a Voltage Regulator
Another use of such a clipper, besides shaping of waveforms, is in limiting the output voltage of a circuit.
If we wish to limit the output voltage to a maximum of +5V, I could use a shunt clipper circuit with VDC =
5V, with the DC source and diode with polarity reversed from what is shown in the above figure.
If we wish to limit both the minimum and the maximum output voltage (i.e. to keep |Vout| < Vmax), we
could use two clippers connected back-to-back (with the DC source and the diode reversed in each).
Above: Bidirectional voltage clipper, acting as a voltage regulator. Should any voltage Vin < -V1 or Vin > V2
be applied, its corresponding diode will be in forward bias, shorting the output voltage to either –V1 or
+V2 (in the limit that RL >> Ri). As long as –V1 < Vin < +V2, both diodes are in reverse bias, and the circuit
acts as a standard voltage divider: Vout = Vin*RL/2Ri.
That is, such a voltage regulator can be used to suppress spurious voltages (either positive or negative),
so long as its corresponding diode is capable of handling the excess current limited. Circuits of this type
are useful in surge suppressors.
However, a voltage regulator is also useful in the case that Vin is expected to exceed the clipping voltage.
This is the case, for example, with the rectified AC output of a rectifier/filter combination. While the
output voltage approximates good old DC, there is also a ripple voltage superimposed on top. If I pass
this output through a biased clipper set up so that VDC is less than the minimum time-fluctuating output
of the filtered rectifier, the clipper will ensure that the output voltage is held to a fixed value of VDC: any
time the voltage coming off the capacitor exceeds VDC the diode goes into forward bias and the current
through R increases until the voltage delivered to the load diminishes to VDC.
Above: Voltage-regulated filtered rectifier. The output of the filter stage is shown in the center panel. If
VDC is chosen to be less than the minimum voltage of the rippled output, the output voltage delivered to
the load will be held at a stable value of +VDC.
VI.
The Zener Diode: Voltage Regulation done right!
With all that said, voltage regulator circuits are usually not set up in this way.
Rather, voltage regulators typically use a special type of diode known as a Zener diode. The
schematic symbol for a Zener diode (right) looks very much like that of a normal diode,
although there are some little crossbars that make the cathode bar look like the letter “Z.”
In forward bias, Zener diodes operate very much like normal diodes: they conduct a current that
increases exponentially (via the Shockley model) with the forward voltage drop VD, with typical values of
VD around 0.5-0.7 V for Si-based Zener diodes.
For small reverse bias voltages, Zener diodes also operate very much like normal diodes: they conduct a
very small (and roughly voltage-independent) leakage current, typically on the order of A.
However, when the reverse-bias voltage exceeds the PIV rating, a normal diode will begin to conduct
due to breakdown and will be damaged. A Zener diode will begin conducting as well, but is specially
constructed so that it is not damaged by this operation. And Zener diodes are designed to enter their
breakdown mode at a very precise voltage level (which is a function of the diode’s construction). While
they remain in breakdown mode, the voltage drop across the diode will be at a fixed value known as the
Zener voltage VZ. If the load is connected in parallel with the Zener diode, the voltage delivered to the
load will be very close to VZ, which remains very nearly constant over a wide range of applied currents.
Zener diodes are designed to be used in reverse bias. And, unlike normal diodes, they are designed to
be used in situations in which the reverse-bias voltage will exceed the PIV.
Above: Zener diode voltage regulator. Due to the rectifying action of the first diode, the Zener diode is
always in reverse bias. But whenever the output of the filter stage exceeds VZ, the Zener enters
breakdown mode and begins conducting; the voltage across the Zener is held to a fixed value VZ, with the
remainder dropped across the shunt resistor R. Since the load is connected directly across the Zener, the
output voltage remains at a fixed value Vout = VZ as long as the output of the filter stage stays above VZ.
Zener diodes can also be used – and more effectively than ordinary diodes – in surge suppressors. In
this case two Zener diodes can be used in a back-to-back configuration in order to suppress values of Vin
exceeding preset maxima in either the positive or negative direction. (You have a homework problem
which asks you about such a circuit!)
VII.
Clampers (optional)
Next, let’s consider what happens if the shunt resistor RS in a clipper circuit is replaced by a capacitor. In
this case, we will take advantage of the fact that when the diode is in reverse bias, the source couples
directly to the load, whereas when the diode is in forward bias, the source couples only to the diode leg
of the circuit (since the load is effectively shorted by the diode, and the only voltage going to it comes
from the VDC of the bias source).
Another way to think of this is that when the diode is in forward bias, the capacitor charges from the
source. When the diode is in reverse bias, the capacitor discharges into the load. Hence there is a
charging time constant C which depends only on the resistance of the “left” side of the circuit, and a
discharging time constant d which depends on the load resistance.
As long as Vin(t) exceeds VDC, the diode is in forward bias, so there is a voltage across C which tends to
charge it. But as soon as Vin(t) –VC drops below VDC the diode goes into reverse bias. The output voltage
is then given by VDC – VD. When this happens, the capacitor begins discharging. However, the only way
the capacitor can discharge is through the load resistor RL; if  = RLC >> 1/f, the capacitor cannot
discharge before Vin(t) rises to put the diode in forward bias again (which causes the capacitor to
recharge). The end effect is that the capacitor charges up to a relatively constant voltage V C which
constrains Vout(t) = Vin(t) – VC to be less than VDC - VD, and the output voltage thus follows the input
voltage, but with a DC offset equal to VC, so that the maximum value of Vout is VDC-VD. For this reason,
clampers are sometimes called DC restorers.
Above: Clamper (DC restorer) circuit. The input voltage Vin(t) is shown in the center panel. The diode D1
effectively “clamps” the maximum output voltage to VDC (any more than the diode goes into forward
bias), and the capacitor periodically charges and discharges so that the output voltage Vout(t) “follows”
the input voltage Vin(t), but with an added DC offset so that the maximum value of Vout(t) = VDC.
As with the clipper, reversing the direction of VDC effectively reverses the sign of the offset, so that the
maximum output voltage would be –VDC instead of +VDC. Reversing the direction of D1 changes the
clamper’s maximum output voltage into a minimum output voltage.
So, by judicious use of DC voltages and diodes, one can transform an AC signal to have any amount of DC
offset desired. This proves to be very important when we consider transistors and amplifier circuits: an
amplifier will only properly amplify voltages within a certain range; so if we wish to amplify an AC signal
it must be biased so that the range of input and output voltages (or currents) is kept within the linear
range of the amplifier.
VIII.
Light-emitting Diodes (LEDs)
An LED is a special type of diode which emits light when it is in the forward conduction
regime. That is, when connected to a forward bias, the LED drops a specific voltage VD, and
because of this voltage drop, photons are emitted through a phenomenon called
electroluminescence. Typical LEDs have forward voltage drops on the order of 1.5-2.5 volts, which is
significantly larger than that of most typical Si or Ge diodes. LEDs, rather than using Si or Ge, typically
are made using “III-V” or “II-VI” semiconductors such as doped forms of GaAs, or ZnSe or ZnTe. These
materials have larger gaps between the valence and conduction bands than do Si or Ge, which explains
why the forward voltage drops are larger, and why visible-light photons are produced.
LEDs have a number of significant advantages over other light sources. Unlike incandescent lamps, they
are highly efficient, converting a high percentage of the dissipated electrical energy into visible light.
Unlike fluorescent tubes and halogen lamps, they are solid-state devices with no moving parts, and do
not depend on the integrity of a glass tube to maintain a thin gaseous vapor. And in addition, since LEDs
only light up in forward bias, they are sensitive to the direction of the input current, and can be used as
polarity detectors.
LEDs are typically used as indicators, to indicate whether power is being delivered to a circuit, or to
indicate the status of a device.
In early days, the only colors of LEDs available were red and infrared. But more recently, LEDs in other
colors – orange, amber, green, and most recently, blue, ultraviolet, and broadband LEDs emitting
“white” light – have become available.
For this reason LEDs have started to displace incandescent and fluorescent bulbs in a number of
applications.
LEDs, like most normal diodes, are rated both in terms of maximum reverse voltages, and in terms of
maximum forward currents and power dissipation. Since, as with all other diodes, the current drawn
increases exponentially with forward voltage, LEDs generally must be protected by a current-limiting
resistor connected in series with it.
IX.
Other Specialty Diodes (optional)
A number of other specialty diodes have been developed.
Current-limiting diodes (or constant-current diodes) are diodes whose I-V characteristic curve flattens
out at a certain level of current. That is, no matter how high a forward voltage is applied (within reason,
of course!) the maximum forward current drawn tops out at some characteristic level; any device
connected in series with the constant-current diode will also have its current limited to that level. These
diodes may be used in a number of circuits in which a maximum current draw is needed, and in some
ways are analogous to Zener diodes (whose reverse voltage “tops out” at a certain level, and maintain
the voltage applied to any load in parallel with them to a level approximately equal to the Zener voltage
VZ).
A host of issues arise when diodes are used at high frequencies, which give rise to a number of other
specialty diodes.
For one, diodes have a finite amount of capacitance across their junction when operating in reverse bias
mode (since the depletion region is, for all intents and purposes, a capacitor since you have charges of
opposite signs accumulating on either side of an insulating barrier). At high frequencies this capacitance
(typically on the order of 100 pF) gives rise to a leakage current in reverse bias, which defeats the
purpose of having a diode in the first place.
You can also think about this as an effect of “recovery time.” That is, when a diode changes from
forward bias to reverse bias, there is a finite amount of time required for the depletion region to reform, and for the diode to stop conducting, sort of like the “RC time constant.” As frequency increases,
and 1/f becomes comparable to or larger than the recovery time, the diode effectively remains in
forward conduction mode over the entirety of the cycle, since there is never enough time for the
depletion region to regrow. Hence the diode ceases to function as advertised.
Several types of diodes have been developed which attempt to circumvent these limitations, so that
they can be used at high frequencies.
Foremost among these is the Schottky diode, which features a very small junction capacitance, a very
short reverse recovery time, and a moderately small forward voltage drop (VD is typically on the order of
0.2 V). These diodes are used in place of “standard” diodes in very high-frequency applications due to
their superior properties in such circuits. Schottky diodes employ a junction between a doped piece of
semiconductor and a metal, rather than two differently-doped semiconductors, and this difference gives
rise to their unique properties.
The tunnel diode also sees extensive use. In the tunnel diode, the I-V curve reverses on itself over some
voltage range, resulting in a region of “negative resistance.” Tunnel diodes are used to form selfresonant oscillating circuits, to produce alternating current signals at very high frequencies.
Varactor diodes are diodes which have a large, and variable, capacitance in reverse bias; the capacitance
depends on the applied voltage. Varactors are also used in place of capacitors in some high-frequency
resonant circuits, in which the capacitance (and thus the resonant frequency) can be adjusted as a
function of the applied DC bias voltage.
Finally, PIN diodes, as the name implies, are diodes with a thin layer of insulating material placed
between the p-type and n-type materials. PIN diodes have a very small amount of capacitance while in
reverse bias, and are often used in very high-frequency switching applications.