# ECE 252 Introduction to Electrical Engineering

## Lesson 17. Solid State Devices

### Diodes

Probably the simplest solid state device is a diode, shown below. Diodes easily carry current in the forward direction, the direction of the arrow, but block current in the reverse direction.  Frequently it is useful to consider the diode as an ideal device.

Ideal diodes have the following properties:

• Zero resistance in the forward direction.
• Infinite resistance in the reverse direction.
• Any current in the forward direction with no voltage drop.
• Zero current in the reverse direction with any voltage drop.
• Acts like a closed switch in the forward direction.
• Acts like an open switch in the reverse direction.

#### Half-Wave Rectifier

Many useful devices can be made from diodes.  One of these is the rectifier, which is used to covert AC to DC.  A half-wave rectifier is shown below. The diode is assumed to be ideal.  When vin is positive, the diode acts like a closed switch, and vout = vin.  When vin is negative, the diode acts like an open switch, and vout = 0.  This is shown in the diagram below. The above diagram shows the input voltage in solid black.  The output voltage is in dashed red.  Note that vout is always positive.  This hump-backed output waveform is occasionally useful.  For example, it could be used to charge a battery.  Nevertheless, it is usually desirable to have a steady DC value.  If a capacitor is added, the waveform can be made more smooth.  The circuit is shown below. Now the job of the diode is to charge the capacitor.  Whenever vin tries to exceed the capacitor voltage, the diode turns on and the capacitor charges.  When vin falls below the capacitor voltage, the diode turns off and the capacitor discharges exponentially through the load (RL).  This is shown in the diagram below. The larger the capacitor, the less drop off in voltage will occur between peaks.

#### Full-Wave Bridge Rectifier

A better rectifier can be made by using both the positive and negative halves of the sine wave.  A full-wave bridge rectifier is shown below. When vin is positive, diodes D1 and D3 turn on, allowing current to flow downward through the load RL.  In the negative half of the cycle, diodes D2 and D4 turn on, once again causing current to flow downward through the load.  A diagram of the voltage developed by this circuit is shown below. Naturally, this wave can also be smoothed by the addition of a capacitor.  A problem with this circuit is that a common ground cannot be used.  The source vin and the load RL cannot both be grounded, as this would short out the diode D3.

#### Clamping Circuit

Signals coming out of such devices as amplifiers are frequently centered around zero.  Sometimes it is desirable to shift those signals upward so that their voltages are always positive.  For example, A/D converters often expect an input that has no negative values.  The clamping circuit is one way of getting this voltage shift.  A typical circuit is shown below. In this circuit, the source is shown as a 2 V sinusoid.  In general, the input could be any time-varying signal.  When vin goes negative, the diode turns on and the capacitor charges up.  After that, the output vout will be vin + vC.  The diagram below illustrates this process. In this particular example, the diode turns on after the first half cycle.  It then charges up to 2 V.  After that, the diode remains off, and the output is nothing more than the input plus 2 V.  This is actually an oversimplification that will only work perfectly if RL is infinite.  For finite values of RL, the diode will turn on briefly every cycle to recharge the capacitor, and the wave will be flattened at zero during this recharging time.

#### Real Diodes

In some cases, the behavior of a diode cannot be assumed to be ideal.  Almost all commercial diodes are made from silicon.  In particular, if the system voltage is low, the forward voltage drop across a silicon diode cannot be ignored.  The forward voltage is the voltage drop across the diode while it is conducting in the forward direction.  Although the voltage depends (nonlinearly) on current, a typical approximation is that the forward voltage drop (at any current) is 0.7 V.  The diagram below illustrates this situation. By Kirchhoff's Voltage Law:

-2 + .7 + vout = 0
vout = 1.3 V

The half-wave rectifier was originally analyzed as though the diode were ideal.  If we analyze it as a silicon diode instead, the waveform looks as shown below. The output voltage is 0.7 V lower than the input voltage during part of positive half of the wave.  The output voltage never goes negative.

Designers of diode circuits must also take into account the maximum current the diode can carry without damage to the diode.  Basically, the diode cannot be allowed to get too hot.  In the specification sheet for the diode, look for "average forward current" or something like it.  There may be other current specifications as well, such as "non-repetitive peak forward current," but the average current is usually the more important specification.  This specification typically assumes that the diode has a good heat sink.  The current can be allowed to exceed this average for short periods of time, but a conservative design, particularly one without a heat sink, will not allow the current to reach the "average forward current" limit.

As an example, let's make a current calculation for the half-wave rectifier.  The peak voltage across the load is 1.3 V.  The current is therefore:
Imax = 1.3/RL

The 1N4148 diode has an average forward current of 150 mA.  If that diode is used, we can calculate the minimum value of RL:
RL = 1.3/(average forward current) = 1.3/150 mA = 8.7 Ω

If RL is smaller than this value, the diode may be damaged.

Another specification may become important in high-voltage circuits:  peak inverse volts (PIV).  This is the maximum reverse voltage that can be placed on the diode without its breaking down.  For example, the 1N4148 has a PIV of 100 V.  A good designer will always check the specification sheet for a diode before putting it into a circuit.

#### LEDs

Although light-emitting diodes (LEDs) are certainly diodes, we will treat them separately because they are usually used for their light-emitting properties rather than their diode properties.  The electronic symbol for an LED is shown below. When current flows through the diode, it lights up - the greater the current, the brighter the light.

Recall that silicon diodes have a forward voltage drop of about 0.7 V.  LEDs are made of various semiconducting materials, depending on the wavelength of light desired.  A typical red LED, made of aluminum-gallium-arsenide, has a forward voltage drop of about 2 V.  A typical blue-white LED may have a forward voltage drop of about 4 V.

In almost all LED circuits, a series resistor is needed to limit the current.  You must consult the specification sheet for the diode to determine how much current it can safely carry.  A typical diode may have a maximum current of 20 mA.

You should avoid wasting energy in heating the series resistor.  One technique for reducing the resistive losses is to use multiple LEDs in series.  Example:  You have a number of red LEDs with a forward voltage drop of 2 V and a maximum current of 20 mA.  You want to connect them to a 9 V battery.  Solution:  Use 4 LEDs in series, which will provide a voltage drop of 4 x 2 = 8 V.  The remaining 1 V will occur across the series resistor.  If the current in the circuit must be no more than 20 mA, the resistor should have a value of 1V/20 mA = 50 Ω or more.  The circuit is shown below. Before going on, you should complete Tutorial 17 on diodes.

### Bipolar Junction Transistors

One of the earliest transistors, widely used since 1950, is the bipolar junction transistor (BJT).  The circuit symbol for an NPN (negative-positive-negative) BJT is shown below. The PNP (positive-negative-positive) transistor looks just like it except that the arrow points into the base.

The BJT is a current amplifier.  Current flowing into the base (iB) is amplified to produce the collector current (iC).  The relevant equations are:

iC = βiB
iE = iB + iC

The constant β is technically called the common-emitter current gain, but we will just refer to it as the gain.  In datasheets, β is often referred to as hFE.  β has a typical value between 10 and 100.  To illustrate the use of these formulas, consider the typical application below. This is the so-called common emitter configuration, meaning that the emitter of the transistor is connected to ground.  VCC is the collector supply voltage; this voltage is needed to provide power for the circuit.  Vo is the output voltage.

Assume VCC is 9 V, RC is 6.8 kΩ, iB is 20 μA, and β is 15.

iC = βiB = 15(20 μA) = 300 μA

The voltage across RC is:

VRc = (6.8 k)(300 μ) = 2.04 V

By Kirchhoff's Voltage Law, the output voltage is:

Vo = VCC  -  VRc = 9 - 2.04 = 6.96 V

If the input that  produces iB is a signal of some sort, you should see how that signal could be amplified and converted into a voltage.

Another typical BJT circuit is the common collector configuration, shown below. In this example, assume that iB is produced by a sensor with a voltage Vi of 3 V and an internal Thevenin resistance RB of 200 kΩ.  Assume VCC is 9 V, RE is 50 kΩ, and β is 85.   For this analysis, we shall also assume that the base-to-emitter voltage is zero, although it is actually about 0.7 V (the same as for a forward-biased silicon diode).

By Kirchhoff's Voltage Law:

-Vi + iBRB + iERE = 0

We know that:

iC = βiB
iE = iB + iC

Therefore:

-Vi + iBRB + (iB + βiB)RE = 0
-3 + iB200k + (iB + 85iB)50k = 0
-3 + iB(200k + 50k + 4250k) = 0
iB = 3/4500k = 0.667 μA
iE = iB + βiB = .667 + 85(.667) = 57.3 μA
Vo = iERE = (57.3 μA)(50 kΩ) = 2.87 V

This circuit is also called a voltage follower or an emitter follower.  The output voltage is a slightly reduced version of the input voltage - it dropped from 3 V to 2.87 V.  The point of the circuit is not to amplify the voltage, but to reduce the effect of the Thevenin resistance of the source (RB of 200 kΩ in this case) in attenuating the output.  If the sensor had been connected directly to RE instead of through the transistor, the output voltage would have been only 0.6 V.

Before going on, you should complete Tutorial 17A on transistors.

### Amplifiers

Signals, such as those from sensors, are frequently tiny, and require amplification.  Therefore, it is important for engineers to know a little bit about the properties of amplifiers.  Specifications for an amplifier can be found in the amplifier's datasheet.  Some of the more important specs are discussed below.  Not all of these specifications will be on all amplifier datasheets.

Gain.  Voltage gain for an amplifier is usually designated by G, AV, or just A.  It's also called the "amplification factor."  It is the ratio of the output voltage to the input voltage.  The gain is usually large and is given in dB.  A typical value might be 80 dB.

Power Output.  This is the maximum power that the amplifier can put out.  It is given in watts.  A typical value might be 100 W per channel (for a stereo amplifier).

Sensitivity.  This is how faint an input signal can be and still give an acceptable output.  A typical value might be 1 mV for a microphone input or 100 mV for a CD input.  Another way sensitivity is defined is this:  Amplifier sensitivity is the minimum input voltage required to produce maximum rated power when the volume control is set to maximum.

Signal to Noise Ratio (SNR).  This is a measure of how much a signal is corrupted by noise.  It's the ratio of the signal power to the noise power, and is given in dB.   A typical value might be 90 dB.  The higher the value, the better.

Frequency Response.  This is the range of frequencies that can be passed by the amplifier, +/- 3 dB.  For a good audio amplifier the frequency response should be at least 20 Hz to 20 kHz.  Please note that an audio amplifier will not pass DC or slowly changing signals.  The difference between the high and low frequency response is the bandwidth.  For 20 Hz to 20 kHz, the bandwidth would be 19,080 Hz.

Total Harmonic Distortion (THD).  This is a measure of the unwanted harmonics that are introduced by the amplifier.  This will be discussed in more detail later.  This number should be less than 1% for a good audio amplifier.

DC Offset at Output.  In addition to an AC component (the signal part) at the output, there may be a DC component.  The DC part is usually undesirable.  If there is a DC offset, it's not always possible to directly connect the output to a speaker.

Input Impedance.  This is the input impedance of the amplifier.  Usually, high values are preferred.  A typical value might be 50 kΩ.

Output Impedance.  This is the output impedance of the amplifier.  Usually, low values are preferred.  A typical value might be 8 Ω for an audio amplifier.

Sometimes amplifiers are connected together (cascaded amplifiers).  In such cases, the total gain is the product of the individual amplifier voltage gains:

AV = AV1 × AV2

If the gains are in dB, the gains are added instead of multiplied.

When amplifiers are connected together, they are frequently connected with capacitors, as shown below. The capacitors block DC offset voltages from passing between stages.  Capacitor coupling cannot be used for slowly changing signals.

Because there is an upper limit to the frequency response of an amplifier, abrupt changes in the signal will tend to be smoothed out, as shown in the diagram below. tr is the rise time.  As an approximation:

tr = 0.35/BW

Where BW is the bandwidth in Hz.

Harmonic distortion is a phenomenon that occurs in amplifiers because Av (voltage gain) is not constant over all signal amplitudes.  Av tends to decrease at high amplitudes.  Therefore, the tops of waves tend to flatten out.  When a sinusoid is distorted, harmonics appear.  These harmonics are integer multiples of the fundamental frequency.  For example, a distorted 150 Hz sinusoid will have harmonics at 300 Hz, 450 Hz, 600 Hz, etcTotal harmonic distortion (THD) is given by the following formula.

THD = sqrt(D22 + D32 + D42 + ---)

Where Dn = Vn/V1

Vn is the amplitude of the nth harmonic and V1 is the amplitude of the first harmonic (the fundamental).

A good audio amplifier will have a THD less than 1%.

### Solid State Relay

The solid state relay is frequently used as a substitute for older mechanical relays.  There are many different implementations of solid state relays.  A simplified version of one of them is shown below. This device consists of an encapsulated LED and two phototransistors.  When current flows through the LED, light falls on the gates of the phototransistors, and the two load terminals are connected together.

The solid state relay has the following advantages over its mechanical cousin:

• Faster switching
• No moving parts (therefore longer life)
• Bounceless (mechanical relays suffer from contact bounce)
• No inductive kickback
• Silent
• Smaller

Solid state relays are not typically cheaper than mechanical relays, and mechanical relays may be able to carry more current.