Electronic Engineering

Electronic Engineering

© University of Wales Newport 2009 This work is licensed under a Creative Commons Attribution 2.0 License.

The following presentation is a part of the level 5 module -- Electronic Engineering. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1 st year undergraduate programme.

The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments.

Contents Circuit calculations using active non-linear devices. Equivalent Circuits Bipolar Transistor. The Hybrid Parameter Network. The Hybrid Model The electronic equivalent circuit is drawn in the followi... Model at High Frequencies The Miller Effect Field Effect Transistor FET Credits

In addition to the resource below, there are supporting documents which should be used in combination with this resource. Please see:Clayton G, 2000, Operational Amplifiers 4th Ed, Newnes James M, 2004, Higher Electronics, Newnes

Electronic Engineering

Circuit calculations using active non-linear devices.Circuit theorems such as:

Kirchhoff’s Laws Thévenin’s Theorem Superposition

work only if the circuit components are linear i.e. if you double the voltage, you double the current. Components such as resistors, capacitors and inductors are, on the whole linear in nature. When we come to analysing circuits with non-linear components such as diodes, bipolar transistors and field effect transistors we must adopt one of two techniques:

Electronic Engineering

1. Graphical2. Equivalent Circuits

The graphical method uses plots of the input and output characteristics to determine the characteristics of the created amplifier or circuit. This requires a large amount of graphical information to be available especially if a design is being formulated with a wide range of possible devices to be considered.

Electronic Engineering

Electronic Engineering

XIB

Vsupply (Vs)

Vs/RciB

Electronic Engineering

Equivalent CircuitsThe other approach is to use a circuit comprising linear

components, which responds in the same way as the non-linear active device. The equivalent circuit may not be perfect but will often give us a starting point when designing. Note that electronics on the whole is far from exact as we are working with components with relatively high tolerance:

Resistors typically 5% and Capacitors typically 10% as well as active devices which can vary dramatically in terms of their characteristics from one device to another.

Electronic Engineering

Diode

The diode can be modelled using a resistor R, a voltage source E and an ideal diode

The diode D only conducts when the anode is positive with respect to the cathode. The supply E ensures that the anode of D only goes positive when the applied voltage reaches a certain positive level. The resistor R controls the current once the diode is conducting.

RE D

Anode

Cathode

Electronic Engineering

The result is a characteristic that looks like:

E Applied voltage V

Current flow

Slope = 1/R

This type of model is called a small signal model as it has good approximation for a small range of inputs.

This approximates the characteristic for a simple diode where E for Silicon is about 0.6v. Of course this is not exact but is fairly good over the limited range where the diode is conducting.

Electronic Engineering

0

0.5

1

1.5

2

2.5

3

0.4 0.45 0.5 0.55 0.6 0.65

1A

0.05V

0.53V

R = 0.05

Bipolar Transistor.The models for both NPN and PNP are the same. The

models vary subtly for different configurations. We will examine the most common configuration – that of the common emitter.

InputOutput

The input on the left is between the base and the emitter and the output on the right is between the collector and the emitter. The emitter is therefore common to input and output

which gives the configuration the name.There are a number of models that exist for this device. We will look in detail at two of these.

The Hybrid Parameter Network. This replaces the input and the output sides by

conventional circuit theory equivalent circuits.

The input is replaced by a Thévenin equivalent i.e. a resistor in series with a voltage source.

The output part of the transistor is replaced by a Norton equivalent circuit comprising a current source in parallel with a resistor, as shown

If we now combine these we have the Hybrid Parameter Network.

The reason for the choice of equivalent circuits is that the input is voltage driven whilst the output is associated with current flow.

hie

IB IC

VBE VCEhoe

hre x VCE

hfe x IB

Electronic Engineering

There are 4 parameters associated with this model, these being:

hie – hybrid input common emitterThis is a measure of the input resistance of the

transistor and is measured in ohms. It is given by:

hre – hybrid reverse gain common emitterThis is a measure of the effect of the output voltage on

the input and is effectively a reverse voltage gain. It has no units. It is given by:

BBE

IV

CEBE

VV

Electronic Engineering

hfe – hybrid forward gain common emitterThis is a measure of the effect of the input current on

the output and is effectively a forward current gain. It has no units. It is given by:

hoe – hybrid output common emitterThis is a measure of the output conductance of the

transistor and is measured in Siemens. It is given by:

BCI

I

CECV

I

Electronic Engineering

The reason for the resistor on the output being expressed as a conductor will become apparent when we start to generate equations.

By looking at the input side and the output side we can generate two equations, these are

Input side:VBE = hie x IB + hre x VCE

Output sideIC = hfe x IB + hoe x VCE

The symmetry between the equations can be seen – this would not be true if hoe were quoted as a resistor.

If we wish to measure the four parameters then we can see how this can be done using the equations:

VBE = hie x IB + hre x VCEIC = hfe x IB + hoe x VCE

hie = VBE/IB as long as VCE is zerothis is written as:

hie = VBE/IB |VCE = 0

What are the equations for the other three?

In any circuit containing a common emitter transistor, the transistor can now be replaced by the four interconnected components.

NOTES.1. This is a small signal model and only works

effectively over a limited range of input conditions.2. This is an a.c. model and cannot be used to set up

the initial d.c. conditions around the transistor (i.e. biasing)

3. This model does not take into account variations in frequency and can only be used within the normal operating frequencies of the amplifier.

4. All capacitors in the transistor circuit are considered to be short circuits when constructing the equivalent circuit.

5. All d.c. power supplies act as large capacitors and can therefore also be thought of as short circuits.

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We are now ready to start analysing transistor circuits but before we do here are some typical values for the parameters:

This is for a BC107 – other transistor values can be found in manufacturer’s literature.

Parameter Value

hie 1 k

hre 3 x 10-4

hfe 250

hoe 300 S

NOTE – The values are typical values for that device and will vary considerably.

Electronic Engineering

Example

Vs

RcRb1Vout

Rb2 Re Ce

Vin

Ground

Rb1 = 68k

Rb2 = 27k

Rc = 1.8k

Re = 1k

Ce = 100F

Other caps = 0.1F

Vs = 9vInput is a voltage source with an internal resistance of 50

Output is a 120 loudspeaker Electronic Engineering

The Hybrid Model This is model based on the physical construction of

the transistor. A typical transistor has the following construction:

Emitter Collector

Base

rbb’

rb’crb’e

rce

Cb’cCb’e

b’

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From the diagram:rbb’ this is the resistance from the base

connection to the centre of the base region.rb’e this is the resistance from the centre of the

base to the emitter connection.rb’c this is the resistance from the centre of the

base to the collector connection.rce this is the resistance from the collector

connection to the emitter connection.Cb’e this is the junction capacitance of the base

emitter junction.Cb’c this is the junction capacitance of the base

collector junction.The current generator has a value given by gM x Vb’e.

gM is called the transistors transconductance.

Typical values for the device are:

Parameter Value

rbb’ 300 rb’e 2000 rb’c 1.5 Mrce 25 k

Cb’e 8 pF

Cb’c 4 pF

gM 0.125 S

Electronic Engineering

The electronic equivalent circuit is drawn in

the following way: IC

VBE VCErce

rb’crbb’

rb’eCb’e

Cb’c

gM x Vb’e

Vb’e

b b’ c

e

Hybrid Hybrid -

hie rbb’ + rb’e

hre rb’e/rb’c

hfe gM x rb’e

hoe 1/rce

It is possible to draw some comparisons between the two models and in doing so we can equate certain components:

When we are working at low to medium frequencies, the capacitors will have relatively high values:

Cb’e = 8 pF will have a reactance at 20 kHz of1/2fC = 995 k

This is so large compared to the other resistors both of the capacitors and rb’c are removed giving us:

IC

VBE VCErce

rbb’

rb’e

gM x Vb’e

Vb’e

b b’ c

e

This model is now very similar to the original H parameter model.

Electronic Engineering

Model at High FrequenciesAt higher frequencies the reactance of the capacitors

begins to drop and their effect increases. What they effectively do is reduce the current flow through Rb’e by allowing it to flow via other paths as shown.

IC

VBE VCErce

rb’crbb’

rb’eCb’e

Cb’c

gM x Vb’e

Vb’e

b b’ c

e

Electronic Engineering

We need to determine the flow through Cb’c Note. The transistor amplifier inverts the signal as it

amplifies which means that as the input goes positive the output goes negative. The upshot of this is that the voltage across Cb’c is given by:Vb’e + Vce but Vce = gain x Vb’e so this gives usVb’e + Vb’e x gain = Vb’e (1 + gain)

an approximation for the gain is gM x RL so

Voltage across Cb’c = Vb’e (1 + gM x RL)

Which means the current is Vb’e (1 + gM x RL) j Cb’c

This has the same effect as a capacitor from b’ to e whose value is:

Cb’c x (1 + gM x RL)Electronic Engineering

The input part of the circuit can therefore be redrawn as:

VBE

rbb’

rb’eVb’e

b b’

Cb’e

Cb’c x (1 + gM x RL)

The two capacitors in parallel can now be combined to given a single capacitor CIN given by

Cb’e + Cb’c x (1 + gM x RL)What has effectively happened is that the value of the feedback capacitor has been amplified and applied across the input. This is called the Miller Effect.

Electronic Engineering

The Miller Effect If we have an inverting amplifier with a capacitor

connected between it’s input and output then this is equivalent to the amplifier with one capacitor connected from its input to ground and another between its output and ground.

The value of the input capacitor is C (A + 1) and the output capacitor is given by C (A + 1)/A

A A

C

~AC

~C

Electronic Engineering

Going back to our amplifier; it is important to know the frequency at which the

amplifiers gain begins to reduce due to the effect of the capacitors. The point at which we define the amplifier to be beyond it’s working limit, i.e. outside its bandwidth, is when the resistance of rb’e equals the reactance of CIN. (This is the amplifiers -3dB point)

rb’e = 1/(2fCIN) from which we can say that the break frequency for the amplifier is:f = 1/(2CIN rb’e)

Electronic Engineering

Field Effect Transistor FET

The equivalent circuit of an FET is relatively simple compared to the bipolar transistor. The circuit below shows the complete model.

ID

VGSVDSrds

gM x VGS

Gate Drain

Source

Cgs

CgdTypical Values for the parameters are:

rds 100KCgs 4 pFCgd 1 pFgM 5mS

Electronic Engineering

At low frequencies the model simplifies to become:

ID

VGSVDSrds

gM x VGS

Gate Drain

SourceIf we have load RL and RL << rds then:

VDS = gM VGS RL

Giving Gain = VDS/VGS = gM RL

At high frequencies the Miller effect can once again be used to give us an equivalent input capacitance of:

Cin = Cgs + Cgd (1 + gM RL)Electronic Engineering

If we have a Voltage Source connected to the input then the input circuit becomes:

Cin

RS

VS

~

VGS

Reactance of the capacitor is

therefore

this gives us a gain of:

Cinj1

CinjRs

CinjVsVgs

1

1

CinRsjVsVgs

1

1

CinRsj

RlgmGain

1This produces a gain that

rolls off above a certain frequency.

This resource was created by the University of Wales Newport and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.

© 2009 University of Wales Newport

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Electronic Engineering