H. Chan; Mohawk College 1 ELECTRONIC CIRCUITS EE451

H. Chan; Mohawk College1

ELECTRONIC CIRCUITSELECTRONIC CIRCUITSEE451

H. Chan; Mohawk College 2

MAIN TOPICS (2nd half)MAIN TOPICS (2nd half)

Analog & Switching Power Supplies Review of rectification & filtering Review of zener diode as a voltage regulator Transistor series shunt voltage regulators Transistor current regulators IC voltage regulators (e.g. 78/79XX, LM317) Switching-mode regulators (e.g. LH1605)

Linear Integrated Circuit Applications BiFET & Norton op-amps, 555 timer, 8038 function

generator, active filters, etc.


Power Supply Block DiagramPower Supply Block Diagram


Half-Wave RectifierHalf-Wave Rectifier

7.0V2VSP

FL

Pdc CR

00833.01VV

FL

P

r CR

V0048.0V

V

t


Full-Wave RectifierFull-Wave Rectifier

7.0V707.0VsP

FL

Pdc CR

00417.01VV

FL

P

r CR

V0024.0V

V

t


Bridge-Type RectifierBridge-Type Rectifier

4.1V2VsP

FL

Pdc CR

00417.01VV

FL

P

r CR

V0024.0V

V

t


More Equations . . . More Equations . . .

Rearranging the previous equations: VP = Vdc + 1.736 Vr

The ripple voltage as a percentage of the dc voltage is:

100% xV

Vripple

dc

r

The diode(s) must be rated to withstand the surge current:

W

Psurge R

VI

where RW is the transformer winding’sresistance given by:

FL

FLNLW I

VVR


Comparison of Different Types of RectifiersComparison of Different Types of Rectifiers

Half-wave rectifier needs only a single diode but ripple is twice those of the other types.

Full-wave rectifier requires a centre-tapped transformer and its output voltage is about half those of the other types.

Bridge-type rectifier is best overall even though it requires four diodes because the diode bridge is often available in a single package. However, if a single diode in the bridge is defective, the whole package has to be replaced.


Line RegulationLine Regulation

i

o

V

VVmVregulationLine

)/(

oi

o

Vx

V

Vregulationline

100%

is a measure of the effectiveness of a voltage regulatorto maintain the output dc voltage constant despitechanges in the supply voltage.


Load RegulationLoad Regulation

is a measure of the ability of a regulator to maintain aconstant dc output despite changes in the load current.

L

o

I

VAmVregulationLoad

)/(

oL

o

Vx

I

Vregulationload

100%


Other SpecificationsOther Specifications

A common definition for voltage regulation is:

100(%) xV

VVregulationVoltage

FL

FLNL

The ability to reduce the output ripple voltage is:

)(

)(log20)(inr

outr

V

VdBrejectionRipple

Source resistance of regulator is:

morI

VR

L

os


Zener Diode Voltage RegulatorZener Diode Voltage Regulator

Circuit

I-V Characteristic

IZM


Notes on Zener Diode RegulatorNotes on Zener Diode Regulator

VZ depends on I and temperature. Zener diodes with rated voltage < 6 V have negative

temperature coefficient; those rated > 6 V have positive temperature coefficient.

In order to maintain a constant Vo, IZT varies in response to a change of either IL or Vi. For example, when RL increases, IL decreases, then IZT has to increase to keep the current through Rs constant. Since the voltage drop across Rs is constant, Vo stays constant.


Formulae for Zener Regulator CircuitFormulae for Zener Regulator Circuit

Rs establishes the zener bias current, IZT:

LZT

Zi

Rs

Zis II

VV

I

VVR

For fixed Vi, but variable RL:

ZMRs

Z

L

ZL

Zi

Zs

Rs

ZL

II

V

I

VR

VV

VR

I

VR

(min)

.max

.min


Formulae (cont’d)Formulae (cont’d)

For fixed RL, but variable Vi:

LZMR

ZsRi

ZL

sLi

IIIwhere

VRIV

VR

RRV

(max)

(max).max

.min

The output ripple voltage of the zener regulator is:

)()( //

//inr

sZL

ZLoutr V

RRR

RRV

where RZ = ac resistance

of zener diode.


Transistor Series Voltage RegulatorTransistor Series Voltage Regulator

The simple zener regulatorcan be markedly improvedby adding a transistor.Since VBE = VZ - VL anytendency for VL to decrease or increase will be negatedby an increase or decrease in IE. The dc currents for thecircuit are:

R

VVI

R

VV

R

VI Zi

RL

BEZ

L

LL

;

IL = hFEIB; IZT = IR - IB


Transistor Shunt Voltage RegulatorTransistor Shunt Voltage Regulator

Since VBE = VL - VZ,any tendency for VL

to increase or decreasewill result in a corresponding increase or decrease in IRs. This willoppose any changes in VL because VL = Vi - IRsRs.

S

BEZi

Rs

L

BEZ

L

L

L R

)VV(VI;

R

VV

R

VI

IE = IRs - IL = hFEIZT


Op-Amp Voltage RegulatorsOp-Amp Voltage Regulators

Zo VR

RV

3

21

Series Shunt


Notes on Op-Amp Voltage RegulatorNotes on Op-Amp Voltage Regulator

More flexibility possible in design of voltage output than IC voltage regulator packages.

The essential circuit elements are: a zener reference, a pass or shunt transistor, a sensing circuit, and an error/amplifier circuit.

Equation indicates that Vo depends on R2, R3, and VZ.

The shunt configuration is less efficient but R2 offers short-circuit current limiting.


Constant Current LimitingConstant Current Limitingcan be used for short-circuit or overload protection ofthe series voltage regulator.

4(max)

7.0

RIL

Output currentis limited to:


Fold-back Current LimitingFold-back Current Limitingis a better method of short-circuit protection.

oLooBBE VRIVRR

RVVV

)( 4

65

622


Design Equations for Fold-back Current LimitingDesign Equations for Fold-back Current Limiting

Maximum load current without fold-back limiting:

64

655(max)

)(7.0

RR

RRVRI o

L

Output voltage under current limiting condition:

L

Lo RRRR

RRRV

564

65 )(7.0'

The short circuit current (i.e. when Vo = 0) is:

64

65 )(7.0

RR

RRI short


Characteristics of Fold-back LimitingCharacteristics of Fold-back Limiting

Notice that Ishort < IL(max) and that Vo is regulated (i.e. constant) only after RL > a certain critical value.

For designing purpose, R5 + R6 = 1 k and if Ishort and IL(max) are specified then

(max)4 7.0)7.0(

07

Loshort

o

IVI

VR

Vo

IL


Transistor Current RegulatorsTransistor Current Regulatorsare designed to maintain a fixed current through aload for variations in either Vi or RL.

For the BJT circuit, VEB = VZ - VRE.Any tendency for IL to change willcause an opposing change in VEB,thus nullifying the perturbation.

For the JFET circuit, IL = ID = IDSS aslong as VL < VSS - VP.


IC Voltage RegulatorsIC Voltage Regulators

There are basically two kinds of IC voltage regulators: Multipin type, e.g. LM723C 3-pin type, e.g. 78/79XX

Multipin regulators are less popular but they provide the greatest flexibility and produce the highest quality voltage regulation

3-pin types make regulator circuit design simple


Multipin IC Voltage RegulatorMultipin IC Voltage Regulator

LM 723C Schematic

The LM723 has an equivalent circuit that contains most of the parts of the op-amp voltage regulator discussed earlier.

It has an internal voltage reference, error amplifier, pass transistor, and current limiter all in one IC package.


Notes on LM723 Voltage RegulatorNotes on LM723 Voltage Regulator

Can be either 14-pin DIP or 10-pin TO-100 can May be used for either +ve or -ve, variable or

fixed regulated voltage output Using the internal reference (7.15 V), it can

operate as a high-voltage regulator with output from 7.15 V to about 37 V, or as a low-voltage regulator from 2 V to 7.15 V

Max. output current with heat sink is 150 mA Dropout voltage is 3 V (i.e. VCC > Vo(max) + 3)


LM723 in High-Voltage ConfigurationLM723 in High-Voltage Configuration

External pass transistor andcurrent sensing added.

Design equations:

2

21 )(

R

RRVV ref

o

21

213 RR

RRR

max

7.0

IRsens

Choose R1 + R2 = 10 k,and Cc = 100 pF.To make Vo variable,replace R1 with a pot.


LM723 in Low-Voltage ConfigurationLM723 in Low-Voltage Configuration

With external pass transistorand foldback current limiting

sens5

54o4

(max)L RR

)RR(7.0VRI

sens5

54

short RR

)RR(7.0I

(max)Loshort

o

sens I7.0)7.0V(I

V7.0R

L4sens5

54L

o RRRR

)RR(R7.0'V

Under foldback condition:

21

ref2

o RR

VRV


Three-Terminal Fixed Voltage RegulatorsThree-Terminal Fixed Voltage Regulators

Less flexible, but simple to use Come in standard TO-3 (20 W) or TO-220 (15 W)

transistor packages 78/79XX series regulators are commonly available

with 5, 6, 8, 12, 15, 18, or 24 V output Max. output current with heat sink is 1 A Built-in thermal shutdown protection 3-V dropout voltage; max. input of 37 V Regulators with lower dropout, higher in/output, and

better regulation are available.


Basic Circuits With 78/79XX RegulatorsBasic Circuits With 78/79XX Regulators

Both the 78XX and 79XX regulators can be used to provide +ve or -ve output voltages

C1 and C2 are generally optional. C1 is used to cancel any inductance present, and C2 improves the transient response. If used, they should preferably be either 1 F tantalum type or 0.1 F mica type capacitors.


Dual-Polarity Output with 78/79XX RegulatorsDual-Polarity Output with 78/79XX Regulators


78XX Regulator with Pass Transistor78XX Regulator with Pass Transistor

Q1 starts to conduct when VR2 = 0.7 V.

R2 is typically chosen so that max. IR2 is 0.1 A.

Power dissipation of Q1 is P = (Vi - Vo)IL.

Q2 is for current limiting protection. It conducts when VR1 = 0.7 V.

Q2 must be able to pass max. 1 A; but note that max. VCE2 is only 1.4 V.

max1

7.0

IR

22

7.0

RIR


78XX Floating Regulator78XX Floating Regulator

It is used to obtain an output > the Vreg value up to a max.of 37 V.

R1 is chosen so that

R1 0.1 Vreg/IQ, where IQ is the quiescent current of the regulator.

21

RIR

VVV Q

regrego

1

12

)(

RIV

VVRR

Qreg

rego

or


3-Terminal Variable Regulator3-Terminal Variable Regulator

The floating regulator could be made into a variable regulator by replacing R2 with a pot. However, there are several disadvantages: Minimum output voltage is Vreg instead of 0 V.

IQ is relatively large and varies from chip to chip.

Power dissipation in R2 can in some cases be quite large resulting in bulky and expensive equipment.

A variety of 3-terminal variable regulators are available, e.g. LM317 (for +ve output) or LM 337 (for -ve output).


Basic LM317 Variable Regulator CircuitsBasic LM317 Variable Regulator Circuits

Circuit with capacitorsto improve performance

Circuit with protectivediodes

(a) (b)


Notes on Basic LM317 CircuitsNotes on Basic LM317 Circuits

The function of C1 and C2 is similar to those used in the 78/79XX fixed regulators.

C3 is used to improve ripple rejection. Protective diodes in circuit (b) are required for

high-current/high-voltage applications.

21

RIR

VVV adj

refrefo

where Vref = 1.25 V, and Iadj isthe current flowing into the adj.terminal (typically 50 A).

1

12

)(

RIV

VVRR

adjref

refo

R1 = Vref /IL(min), where IL(min)

is typically 10 mA.


Other LM317 Regulator CircuitsOther LM317 Regulator Circuits

Circuit with pass transistorand current limiting

Circuit to give 0V min.output voltage


Block Diagram of Switch-Mode RegulatorBlock Diagram of Switch-Mode Regulator

It converts an unregulated dc input to a regulated dcoutput. Switching regulators are often referred to asdc to dc converters.


Comparing Switch-Mode to Linear RegulatorsComparing Switch-Mode to Linear Regulators

Advantages: 70-90% efficiency (about double that of linear ones) can make output voltage > input voltage, if desired can invert the input voltage considerable weight and size reductions, especially at

high output power

Disadvantages: More complex circuitry Potential EMI problems unless good shielding, low-loss

ferrite cores and chokes are used


General Notes on Switch-Mode RegulatorGeneral Notes on Switch-Mode Regulator

The duty cycle of the series transistor (power switch) determinesthe average dc output of the regulator. A circuit to control theduty cycle is the pulse-width modulator shown below:


General Notes cont’d . . . General Notes cont’d . . .

The error amplifier compares a sample of the regulator Vo to an internal Vref. The difference or error voltage is amplified and applied to a modulator where it is compared to a triangle waveform. The result is an output pulse whose width is proportional to the error voltage.

Darlington transistors and TMOS FETs with fT of at least 4 MHz are often used. TMOS FETs are more efficient.

A fast-recovery rectifier, or a Schottky barrier diode (sometimes referred to as a catch diode) is used to direct current into the inductor.

For proper switch-mode operation, current must always be present in the inductor.


Step-Down or Buck ConverterStep-Down or Buck Converter

When the transistor is turned ON, VL is initially high but falls exponentially while IL increases to charge C.

When the transistor turns OFF, VL reverses in polarity to maintain the direction of current flow. IL decreases but its path is now through the forward-biased diode, D.

Duty cycle is adjusted according to the level of Vo.


V & I Waveforms for Buck RegulatorV & I Waveforms for Buck RegulatorPWMoutput

VL

IL

Vo

Normal Low Vo High Vo


Equations for Buck RegulatorEquations for Buck Regulator

T

t

tt

t

V

V on

offon

on

i

o

Selecting IL = 0.4Io where Io

is the max. dc output current:

oscio

oio

fVI

VVVL

)(5.2

oscrms

o

oscpp

o

fV

Ior

fV

IC

01768.005.0

where V is the ripple voltage


Notes on Operation of Buck RegulatorNotes on Operation of Buck Regulator

When IL = 0.4Io was selected, the average minimum current, Imin, that must be maintained in L for proper regulator operation is 0.2Io.

If IL is chosen to be 4% instead of 40% of Io, the 2.5 factor in the equation for L becomes 25 and Imin becomes 0.02Io.

L and C are both proportional to 1/fosc; hence, the higher fosc is the smaller L and C become. But for predictable operation and less audible noise, fosc is usually between 50kHz to 100 kHz.


Step-Up, Flyback, or Boost RegulatorStep-Up, Flyback, or Boost Regulator

Assuming steady-state conditions, when the transistor is turned ON, L reacts against Vin. D is reverse-biased and C supplies the load current.

When the transistor is OFF, VL reverses polarity causing current to flow through D and charges C. Note that Vout is > Vin because VL adds on to Vin.


Equations for Boost RegulatorEquations for Boost Regulator

T

t

V

VV on

o

io

oscoo

ioi

fVI

VVVL

2

2 )(5.2

Assuming IL = 0.4Io:

rmsoosc

oio

ppoosc

oio

VVf

IVVor

VVf

IVVC

)(3536.0)(


Voltage-Inverting or Buck-Boost RegulatorVoltage-Inverting or Buck-Boost Regulator

Vo can be either step-up or step-down and its polarity is opposite to input.

During ON period, Vin is across L, and D is reverse-biased. During OFF period, VL reverses polarity causing current

to flow through C and D.


Equations for Buck-Boost RegulatorEquations for Buck-Boost Regulator

T

t

VV

V on

oi

o

For IL = 0.4Io:

oscioo

oi

fVVI

VVL

)(

5.2

oscoirms

oo

oscoipp

oo

fVVV

VIor

fVVV

VIC

)(

3536.0

)(


Basic Push-Pull Power ConverterBasic Push-Pull Power Converter

Operates as a class D power amplifier. Output rectifier converts the square-wave to dc. Each transistor must withstand 2xVin plusvoltage spikes.


Basic Half-Bridge Power ConverterBasic Half-Bridge Power Converter

Each transistor “sees” approx. Vin. Full flux reversal in the transformer and capacitors across DS prevent voltage spikes.


Basic Full-Bridge Power ConverterBasic Full-Bridge Power Converter

Either Q1 & Q3 or Q2 & Q4 are turned ON simultaneously.Ideal for high power applications.


Single-Package Switch-Mode RegulatorSingle-Package Switch-Mode Regulator

The LH1605 is a 5A step-down switching regulator. Vo is adjustable from 3 to 30 V by using a pot. for R1. In the circuit above, Q1 turns ON when voltage across

Rsens is 0.7 V. Q2 then turns ON shorting Vref to ground and driving Vo to zero. .


Equations for LH1605 Switching RegulatorEquations for LH1605 Switching Regulator

2000800

00125.05.2

1

1

o

o

VR

orRV

oscT f

C40000

1

oscio

oio

fVI

VVVL

)(5.2 With IL = 0.4Io:

oscpp

o

oscrms

o

fV

Ior

fV

IC

05.001768.0

max

7.0

IRsens

Typically, CF = CC = 10 F; RB = 10 k


BiFET IC Operational AmplifierBiFET IC Operational Amplifier

Advantages of TL081 vs bipolar op-amp (LM741): higher input impedance (typically 1012 ) wider unity-gain bandwidth (3 MHz) higher slew rate (13 V/s typical) lower offset current (5 pA) lower bias current (30 pA) lower power consumption (1.4 mA supply current)

All other parameters are comparable to bipolar op-amps.


Frequency CompensationFrequency Compensation

Most op-amps contain a small internal compensating capacitor (15 to 30 pF) for ensuring stability at the expense of bandwidth.

For a specific application requiring a wider bandwidth, an uncompensated op-amp, such as the TL080, may be chosen with a small external compensating capacitor.

Two commonly used methods are: conventional compensation and feed-forward compensation. The latter method can increase the BW 5 to 10 x.


Circuits for Frequency CompensationCircuits for Frequency Compensation

Conventional Feed-forwardC1 is typ.10 to 20 pF C1 is typ. 100 to 150 pF


Response With Frequency CompensationResponse With Frequency Compensation

10k 100k 1M1k 10Mf

Hz

Av

Increase in BW

With feed-forwardcompensation

With normalcompensation


Astable Multivibrator or Relaxation OscillatorAstable Multivibrator or Relaxation Oscillator

Circuit Output waveform


Equations for Astable MultivibratorEquations for Astable Multivibrator

21

2

21

2 ;RR

RVV

RR

RVV sat

LTsat

UT

1

2121

2ln2

R

RRttT Assuming

|+Vsat| = |-Vsat|

If R2 is chosen to be 0.86R1, then T = 2RfC and

where = RfC

CRf

f2

1


Monostable (One-Shot) MultivibratorMonostable (One-Shot) Multivibrator

Circuit Waveforms


Notes on Monostable MultivibratorNotes on Monostable Multivibrator

Stable state: vo = +Vsat, VC = 0.6 V Transition to timing state: apply a -ve input pulse such

that |Vip| > |VUT|; vo = -Vsat. Best to select RiCi 0.1RfC. Timing state: C charges negatively from 0.6 V through

Rf. Width of timing pulse is:

LTsat

satfp VV

VCRt

||

6.0||ln

Recovery state: vo = +Vsat; circuit is not ready for retriggering until VC = 0.6 V. The recovery time tp. To speed up the recovery time, RD (= 0.1Rf) & CD can be added.

If we pick R2 = R1/5, then tp = RfC/5.


Norton or Current-Mode Op-AmpNorton or Current-Mode Op-Amp

Amplifies I (= I- - I+) between the inputs.

Q3 and D1 form a current mirror (ICQ3 ID1). In practice, two matched transistors are used; the 1st transistor connected as a diode.

Current into base of Q1 IB1 = I.

Note that VB 0.7 for both Q1 & Q2.

Simplified circuit


Notes on LM3900 Op-AmpNotes on LM3900 Op-Amp

Comes in a standard 14-pin DIP quad package. Can operate from a single supply (4 to 32 V) or

dual supplies (±2 to ±16 V). Rin = 1 M, Rout = 8 k Aol = 2800 Unity-gain bandwidth = 2.5 MHz (much better

than the LM741) Not as widely used as voltage op-amps because

circuit designers are less familiar with it.


Norton AmplifiersNorton Amplifiers

Inverting

Non-inverting

Design equations for invertingand non-inverting amplifiersare exactly the same:

Zin = RI ;I

Fv R

RA

Neglecting RS and Ro:

LcLout

IcLin

RfC

RfC

2

1

2

1


Other Design Equations for Norton AmplifierOther Design Equations for Norton Amplifier

Note that if dual polarity supply is used,Voffset can be made to be 0V and Cout

would not be required for both circuits.

Since max. Iin = 20 mA dc,

04.0

4.102.0

7.0

(min)

(min)

CCF

CCB

VR

VR

Also, min. input biascurrent is 200 nA,

nA

VR

nA

VR

CCF

CCB

400

4.1

200

7.0

(max)

(max)

The dc output offset voltage:

7.0)7.0(

B

CCFoffset R

VRV

For max. swing, Voffset = VCC/2, thus

7.02/

)7,0(

CC

FCCB V

RVR


Functional Block Diagram of LM555Functional Block Diagram of LM555


Notes on 555 Timer/Oscillator ICNotes on 555 Timer/Oscillator IC

Widely used as a monostable or astable multivibrator.

Can operate between 4.5 and 16 V. Output voltage is approximately 2 V < VCC. Output can typically sink or source 200 mA. Max. output frequency is about 10 kHz. fo varies somewhat with VCC. Threshold input (pin 6) and trigger input (pin 2)

are normally tied together to external timing RC.


555 as a Simple Oscillator555 as a Simple Oscillator

tch = 0.693(R1 + R2)C1

tdisch = 0.693 R2C1

T = 0.693(R1 + 2R2)C1

21

21

2RR

RR

T

tD ch

Duty cycle is:

Given fo and D,

12

11 693.0

1;

693.0

12

Cf

DR

Cf

DR

oo

Note that D must always be > 0.5.To get 50% duty cycle, R1 = 0,which would short out VCC.


555 Square-Wave Oscillator555 Square-Wave Oscillator

tch = 0.693 R1C1 ; tdisch = 0.693 R2C1

121 )(693.0

1

CRRfo

21

1

RR

RD

12

11 693.0

1;

693.0 Cf

DR

Cf

DR

oo

For 50% duty cycle,

121 386.1

1

CfRR

o


555 as a Timer / Monostable Multivibrator555 as a Timer / Monostable Multivibrator

R2 (typically 10 k) is a pull-up resistor.C2 (typically 0.001 F) is for bypass.Timing starts when trigger input is grounded.

t = 1.1 R1C1

Time pulses from a fews to many minutes arepossible. The mainlimitation for very longtime delays is theleakage in the large-value capacitor requiredfor C1.


ICL8038 Function Generator ICICL8038 Function Generator IC

Triangle wave at pin10 is obtained by linear charge and discharge of C by two current sources.

Two comparators trigger the flip-flop which provides the square wave and switches the current sources.

Triangle wave becomes sine wave via the sine converter .


Notes on ICL8038 ICNotes on ICL8038 IC

To obtain a square wave output, a pull-up resistor (typically 10 to 15 k) must be connected between pin 9 and VCC.

Triangle wave has a linearity of 0.1 % or better and an amplitude of approx. 0.3(VCC-VEE).

Sine wave can be adjusted to a distortion of < 1% with amplitude of 0.2(VCC-VEE). The distortion may vary with f (from 0.001 Hz to 200 kHz).

IC can operate from either single supply of 10 to 30 V or dual supply of 5 to 15 V.


ICL8038 Function Generator CircuitICL8038 Function Generator Circuit

+VCC > Vsweep > Vtotal + VEE + 2where Vtotal = VCC + |VEE|

total

sweepCCo VRC

VVf

12

)(3

where R = RA = RB

If pin 7 is tied to pin 8,

BA

AA

o

RRR

CR

f

215

3

1

For 50 % duty cycle,

1

3.0

RCfo


Active FiltersActive Filters

Active filters use op-amp(s) and RC components. Advantages over passive filters:

op-amp(s) provide gain and overcome circuit losses increase input impedance to minimize circuit loading higher output power sharp cutoff characteristics can be produced simply and

efficiently without bulky inductors Single-chip universal filters (e.g. switched-

capacitor ones) are available that can be configured for any type of filter or response.


Review of Filter Types & ResponsesReview of Filter Types & Responses

4 major types of filters: low-pass, high-pass, band pass, and band-reject or band-stop

0 dB attenuation in the passband (usually) 3 dB attenuation at the critical or cutoff

frequency, fc (for Butterworth filter) Roll-off at 20 dB/dec (or 6 dB/oct) per pole

outside the passband (# of poles = # of reactive elements). Attenuation at any frequency, f, is:

decc

fatdBattenxf

ffatdBatten )(.log)(.


Review of Filters (cont’d)Review of Filters (cont’d)

Bandwidth of a filter: BW = fcu - fcl

Phase shift: 45o/pole at fc; 90o/pole at >> fc

4 types of filter responses are commonly used: Butterworth - maximally flat in passband; highly non-

linear phase response with frequecny Bessel - gentle roll-off; linear phase shift with freq. Chebyshev - steep initial roll-off with ripples in

passband Cauer (or elliptic) - steepest roll-off of the four types but

has ripples in the passband and in the stopband


Frequency Response of FiltersFrequency Response of Filters

f

A(dB)

fc

f

A(dB) HPF

fcl fcu

f

A(dB)BPF

fcl fcu

f

A(dB)

BRF

fc

f

A(dB)LPF

Pass-band

Butterworth

BesselChebyshev


Unity-Gain Low-Pass Filter CircuitsUnity-Gain Low-Pass Filter Circuits

2-pole 3-pole

4-pole


Design Procedure for Unity-Gain LPFDesign Procedure for Unity-Gain LPF

Determine/select number of poles required. Calculate the frequency scaling constant, Kf = 2f Divide normalized C values (from table) by Kf to obtain

frequency-scaled C values. Select a desired value for one of the frequency-scaled C

values and calculate the impedance scaling factor:

valueCdesired

valueCscaledfrequencyK x

Divide all frequency-scaled C values by Kx

Set R = Kx


An ExampleAn Example

Design a unity-gain LP Butterworth filter with a critical frequency of 5 kHz and an attenuation of at least 38 dB at 15 kHz.

The attenuation at 15 kHz is 38 dB the attenuation at 1 decade (50 kHz) = 79.64 dB.We require a filter with a roll-off of at least 4 poles.

Kf = 31,416 rad/s. Let’s pick C1 = 0.01 F (or 10 nF). Then

C2 = 8.54 nF, C3 = 24.15 nF, and C4 = 3.53 nF.Pick standard values of 8.2 nF, 22 nF, and 3.3 nF.

Kx = 3,444Make all R = 3.6 k (standard value)


Unity-Gain High-Pass Filter CircuitsUnity-Gain High-Pass Filter Circuits

2-pole 3-pole

4-pole


Design Procedure for Unity-Gain HPFDesign Procedure for Unity-Gain HPF

The same procedure as for LP filters is used except for step #3, the normalized C value of 1 F is divided by Kf. Then pick a desired value for C, such as 0.001 F to 0.1 F, to calculate Kx. (Note that all capacitors have the same value).

For step #6, multiply all normalized R values (from table) by Kx.

E.g. Design a unity-gain Butterworth HPF with a critical frequency of 1 kHz, and a roll-off of 55 dB/dec. (Ans.: C = 0.01 F, R1 = 4.49 k, R2 = 11.43 k, R3 = 78.64 k.; pick standard values of 4.3 k, 11 k, and 75 k).


Equal-Component Filter DesignEqual-Component Filter Design

2-pole LPF 2-pole HPF

Select C (e.g. 0.01 F), then:

CfR

o2

1

Av for # of poles is given ina table and is the same forLP and HP filter design.

1I

Fv R

RA

Same value R & same value Care used in filter.


Example Example

Design an equal-component LPF with a critical frequency of 3 kHz and a roll-off of 20 dB/oct.

Minimum # of poles = 4Choose C = 0.01 F; R = 5.3 kFrom table, Av1 = 1.1523, and Av2 = 2.2346.

Choose RI1 = RI2 = 10 k; then RF1 = 1.5 k, and RF2 = 12.3 k .

Select standard values: 5.1 k, 1.5 k, and 12 k.


Bandpass and Band-Rejection FilterBandpass and Band-Rejection Filter

fctr fctrfcu fcufcl fcl

f fAtt

enua

tion

(dB

)

Att

enua

tion

(dB

)The quality factor, Q, of a filter is given by:

BW

fQ ctr

where BW = fcu - fcl and

clcuctr fff

BPF BRF


More On Bandpass FilterMore On Bandpass FilterIf BW and fcentre are given, then:

24;

242

22

2 BWf

BWf

BWf

BWf ctrcuctrcl

A broadband BPF can be obtained by combining a LPF and a HPF:

The Q of this filteris usually> 1.


Broadband Band-Reject FilterBroadband Band-Reject FilterA LPF and a HPF can also be combined to give a broadbandBRF:

2-pole band-reject filter


Narrow-band Bandpass FilterNarrow-band Bandpass Filter

CRQ

fBW ctr

12

1

12 21

3

Q

RR

R2 = 2 R1

3

1

1

122

1

R

R

CRfctr

R3 can be adjusted or trimmedto change fctr without affectingthe BW. Note that Q < 1.

C1 = C2 = C


Narrow-band Band-Reject FilterNarrow-band Band-Reject FilterEasily obtained by combining the inverting output of a narrow-band BRF and the original signal:

The equations for R1, R2, R3, C1, and C2 are the same as before.RI = RF for unity gain and is often chosen to be >> R1.

Documents

H. Chan; Mohawk College 1 ELECTRONIC CIRCUITS EE451