ANALOG CIRCUITS

(V18ECET08)

II-B.Tech II- Sem-ECE & ECT

(V18 Regulation)

Prepared

​

Dr.U Yedukondalu

UNIT-1

WAVE SHAPING CIRCUITS

Wave Shaping

Definition: It is the process of changing the shape of input signal with linear / non-linear circuits.

Types:

1. Linear Wave Shaping
2. Non-linear Wave Shaping

Linear Wave Shaping

Definition: The process where by the form of a non-sinusoidal signal is changed by transmission through a linear network is called Linear Wave Shaping.

Types:

1. High Pass RC Circuit.
2. Low Pass RC Circuit.

Non-sinusoidal wave forms

1. Step
2. Pulse
3. Square wave
4. Ramp
5. Exponential wave forms.

Step Waveform

t

t=0

i

V_i=0 t<0

^{V =V} t>0

A step voltage is one which maintains the value zero for all times t<0 and maintains the value V for all times t>0.

V_i

V

Pulse

The pulse amplitude is „V‟ and the pulse duration is t_p.

0≤t≤tp

Otherwise

V_i=V

V_i=0

t=tp

t

V_i

V

t=0

0

Square Wave

• A wave form which maintains itself at one constant level v¹ for a time T₁ and at other constant Level V¹¹ for a time T₂ and which is repetitive with a period T=T₁+T₂ is called a square-wave.

T₁

T₂

Ramp

A waveform which is zero for t<0 and which increases linearly with time for t>0.

V_i

V_i =αt

​

V_i =αt , t>0

0

t

Exponential

0

t

• The exponential waveform input is given by

where T is the time constant of the exponential input

V_i

​

V

High Pass RC Circuit

R

+

V

o

C

+

-

V

i

-

If f=low, X_c becomes high

C act as open circuit, so the V_o=0.

​

If f=high, X_c becomes low

C acts as short circuit, so we get the output.

​

The higher frequency components in the input ^signal appear at the output with less attenuation due to this behavior the circuit is called “High Pass Filter”.

X_C =

1

2ΠfC

Sinusoidal input

+

V

O

i

+

^Vin

_

_

• For Sinusoidal input, the output increases in amplitude with increasing frequency.

C

R

V

in

R - j X_C

V

i =

=

R -

in

j

2πf C

^Vin

i=

R ^⎡ 1-

j

⎤

⎢_⎣

2πfRC^⎥_⎦

O

V_in ×R

^Vin

V =i R=

=

1-

j

2πfRC

⎡ ^j ⎤

^{R ⎢}_⎣^1- 2πfR C^⎥_⎦

V_o= iR

V_O

1

=

^Vin

1+j ^⎛-^f1⎞

⎜ _f ⎟

⎝ ⎠

1

=

V_O

^V in

1 + _⎜

2

⎛ ^f1 ⎞

⎟

⎝ ^f ⎠

θ =-tan ^-1_⎜^⎛-f1⎞ = tan^-1⎛_⎜^{f1 ⎞}

⎝ ^{f ⎟}⎠ ⎝^{f ⎟}⎠

​

At the frequency f = f₁

^Vin

V_{O =}

¹ = ¹ =0.707

1+1 2

A =0.707

At f = f₁ the gain is 0.707 or this level corresponds to a signal reduction of 3

decibels(dB).

∴ f₁ is referred to as Lower 3-dB frequency.

Square wave input

• Percentage Tilt ( ^{0 0} Tilt)

Tilt is defined as the decay in the amplitude of the output voltage wave due to the input voltage maintaining constant level

2

1

X 100

P =

1

V

V −V ¹

1

- T ₁

R C

= V ₁. e

V

'

2

- T ₂

RC

V

'

= V₂ . e

1

2

V

'

- V = V

V - V ^' = V

1 2

(1)

(2)

(3)

(4)

& because of

• A symmetrical square wave is one for which T₁=T₂ =

symmetry V₁ = - V₂

By substituting these in above equation (3)

•

_-T2RC _-

^V=V₁^.e ^V₂

_-T2RC₊

^V=V₁^.e ^V₁

_-T2RC

V=V₁(1+e )

I

Equation (1)

II

ForRC>>^T theequation(I)&(II)becomesas

1

2

V₁ ≅ ^V (1+ ^T

2 4RC 2 4RC

^{) &} V^{1 ≅ V (1- T} )

1

V₁ -V¹

Thepercentage tilt ‘P’ is definedby P=

V

2

× 100

High Pass RC Circuit acts as Differentiator:-

• The time constant of high pass RC circuit in very small in comparison within the time required for the input signal to make an appreciable change, the circuit is called a “differentiator”.
• Under this circumstances the voltage drop across R will be very small in comparison with the drop across C. Hence we may consider that the total input V_i appears across C, so that the current is determined entirely by the capacitance.

and the output signal across R is

• Then the current is i = C

V₀ = iR

V₀ = RC

• hence the output is proportional to the derivative of the input.

Low Pass RC Circuit

C

_X =

1

2Πf

C

​

If f=low, X_c becomes high

C act as open circuit, so we get the output.

​

If f=high, X_c becomes low

C acts as short circuit, so V_o=0.

​

As the lower frequency signals appear at the output, it is called as

“Low pass RC circuit”.

Sinusoidal input

in

V

_× X_C

j X_C

O

V =

R +

j

1

2πfC

C

_X =

in

V

×

1

j ω C

1

O

V =

R +

j ω C

wh

ere

O

^Vin ^Vin

V=

=

jωRC+1 1+j2πfRC

CS

o

V = ¹ i

O

^Vin

V =

1+ j ^f

f

2

2

1

2πRC

where ^{f =}

A = ^VO

^Vin

=

1

1 + j

f

f₂

A

₌ 1

2

_{1 +} ⎛ _f ⎞

⎜ _{f ⎟}

⎝ ² ⎠

θ=- tan ^{-1 ⎛ f}

⎟

⎜_f

⎝_⎞ ² ⎠

and

At the frequency f = f₂

^Vin

V_{O =}

¹ = ¹ =0.707

1+1 2

A =0.707

At f = f₂ the gain is 0.707 or this level corresponds to a signal reduction of 3 decibels(dB).

​

^∴ f₂ or f_h is referred to as upper 3-dB frequency.

Square wave input

⁰ ₀to

• Rise Time( t_r):

The time required for the voltage to rise from 10 90⁰ 0of the final steady value is called “Rise Time”.

^Vd.c.

V’

^V01

^V02

V’

V₂

V₂

V₁

T₁

V’’

T₂

^{= V1 + (V1-V 1 ) .} e ^{-T 1 RC}

The output voltage V₀₁ & V₀₂ is givenby

………………… (1)

………………… (2)

^V01

V

02

^{= V11 + (V2-V 11 ) .} e ^{- T 2 RC}

if we set

and

V₀₁ = V₂ at t=T₁

V₀₂ = V₁ at t= T₁+T₂

1 1

^V₂^{= V +( V1-V )} e

11 11

1

V =^V +( V2-^V )

-

^{- T 1} RC

T

2

RC

e

Since the average across R is zero then the d.c voltage at the output is same as that of the

input. This average value is indicated as Vd.c.

Consider a symmetrical square wave with zero average value, so that

_- T

_V ^⎡_{1 - e} ^{- T} 2RC ^⎤

V = ^{⎢ ⎥}

2

^⎢_⎣1 + e

2RC _⎥⎦

T

V ^⎡ e ^{T 2RC - 1 ⎤}

⎥

V₂ = ₂ ⎢

⎢_⎣e

2RC _{+ 1⎥⎦}

T 4RC

2

2 e^2x + 1

_{V =} V _. e^2x - 1

where x =

2

V = ^V tan hx

2

Low pass RC circuit acts as an integrator

• The time constant is very large in comparison with the time required for the input signal to make an appreciable change, the circuit is called an

“Integrator”.

• As RC>>T the voltage drop across C will be very small in comparison to the voltage drop across R and we may consider that the total input V_i appear and across R, then

V_i =iR

For low pass RC circuit the output voltage V_o is given by

O

V

₌ 1

i dt

_C ∫

O

_{V =} 1 V_i

dt

C^∫R

O

i

_{V =} 1

V dt

RC^∫

Advantages of Integrator over differentiator

• Integrators are almost invariably preferred over differentiators in analog

computer applications for the following reasons.

​

• The gain of the integrator decreases with frequency where as the gain of the differentiator increases linearly with frequency. It is easier to stabilize the former than the latter with respect to spurious oscillations.

​

• As a result of its limited band width an integrator is less sensitive to noise voltages than a differentiator.

​

• If the input wave form changes very rapidly, the amplifier of a

differentiator may over load.

​

• It is more convenient to introduce initial conditions in an integrator.

Non-Linear Wave Shaping

Definition:

​

The process where by the form of a sinusoidal signals are going to be altered by transmission through a non-linear network is called Non-linear Wave Shaping.

Non-linear elements (like Diode, transistor) in combination with resistors can function as clipper circuit.

Types:

1. Clippers.
2. Clampers.

Clipper Classifications

According to biasing, the clippers may be classified as

• Unbiased clippers and
• Biased clippers.

According to configuration used the clippers may be

• Series diode clippers
• Parallel or shunt diode clippers
• A series combination of diode, resistor and reference supply
• Multi-diode clippers consisting of several diodes, resistors

and reference voltages

Contd…

According to level of clipping the clippers may be

​

• Positive clippers
• Negative clippers
• Biased clippers and
• Combination clippers

Clipper

• Clipping circuits are used to remove the part of a signal that is above or below some defined reference level.
• Clippers also known as

Voltage limiters

Current limiters Amplitude selectors Slicers

Unbiased Clippers( Parallel Positive Clippers)

• Without the battery, the output of the circuit below would

be the negative portion of the input wave (assuming the

bottom node is grounded). When vi > 0, the diode is on (short-circuited), vi is dropped across R and vo=0. When vi

<0, the diode is off (open-circuited), the voltage across R is

zero and vo=vi.

Unbiased Clippers( Parallel Negative Clippers)

+ive cycle :- anode is at ground potential and cathode sees variable +ive voltage from 0 to +Vm So complete cycle, the diode is reverse biased and Vo =Vin.At positive peak Vo=+5V

-ive cycle :- anode is at ground potential and cathode sees variable -ive vols from 0 to –Vm. When magnitude of in put volatge i.e / Vin/ >Vd, the diode become forward biased and hence Vo =-Vd =0.7V

Series Positive Clipper

+ive cycle :- anode is at ground potential and cathode sees variable +ive voltage from 0 to +Vm.For comlpete, cycle, diode become reverse biased and hence Vo =0V

-ive cycle :- anode is at ground potential and cathode sees variable -ive voltage from 0 to –Vm. So in complete cycle, the diode is forward biased and Vo= Vin + Vd andAt negative peak, Vo= -Vm+ Vd = -5v

Series Negative clipper

+ive cycle :- anode is at positive potential from 0 to +Vm.For comlpete, cycle, diode become forward biased and hence vo= 5v

-ive cycle :- Cathode is at ground potential and cathode sees variable - ive voltage from 0 to –Vm. So in complete cycle, the diode is Reverse biased and negative peak, Vo= 0

Positive Shunt clipping with zero reference _Rvoltage

D

Vo

Vi

Transfer characteristics equations:

^VO^{=0for V}i^{>0 V}O ^{= V}i ^{for V}i^{< 0}

D– ON

^VO^{=Vγfor V}i ^{>Vγ V}O^=Vi ^{for V}i ^{< Vγ}

D– OFF

[Ideal]

V

O

V

i

V

O

V

i

Slope =1

Vγ

Vγ

Input

Input

​

Output

Positive Shunt clipping with positive reference Voltage

D

Vi ^Vo

Transfer characteristics equations:

V_i < V_R+Vγ

D – OFF

V_O = V_i

D – ON

V_i > V_R+Vγ

V_O = V_R+Vγ

Input

V_R + Vγ _{VR + Vγ} Output

V_O

V_R ^V_O

V_i

Positive Shunt clipping with negative

reference voltage

R

D

V_R

Vi

Vo

Transfer characteristics equation:

V_i > Vγ - V_R

D – ON V_O

D – OFF

= Vγ - V_R V_i < Vγ - V_R V_O = V_i

V_O

V_O

V_i

V

i

Input

Output

V_i

Negative Shunt clipping with zero reference voltage

R

Vi

Vo

D

Transfer Characteristic

Equations:

V_i > -Vγ D – OFF

V_O = Vγ

V_i < -Vγ D – ON

V_O = -Vγ

-Vγ

-Vγ

V_O

V_O

V_i

V_i

Input

Output

Negative Shunt clipping with positive

reference voltage

R

D

V_R

Vi

Vo

Transfer Characteristics

Equations:

D – ON

V_i < V_R-Vγ

V_O = V_R-Vγ

V_i > V_R-Vγ

D – OFF

V_O = V_i

V_R - Vγ

V_O

V_i

V_i

V_O

^DOFF

^DON

Negative Shunt clipping with negative reference voltage

R

D

V

R

Vi

Vo

Transfer characteristic

equations:

D – ON V_O

V_i < -( Vγ + V_R)

= -( Vγ + V_R)

V_i < -( Vγ + V_R) D – OFF

V_O = V_i

V

O

V_O

V_i

V_i

- (Vγ + V_R

Input

Negative Series clipper with zero

reference

R

Vi

Vo

D

Transfer characteristicequations:

V_O

V_O

V_i

V_i

Output

CLIPPING AT TWO

INDEPENDENT LEVELS

R

D

V_R

Vi

Vo

D

V_R

Transfercharacteristic equations:

V

O

V_O

V_i

V_i

Input

Output

V_R

1

Contd..

CLAMPING CIRCUIT

• The need to establish the extremity of the positive (or) negative signal excursion at some reference level. When the signal is passed through a capacitive coupling network such a signal has lost its d.c. component. The clamping circuit introduces the d.c. components at the outside, for this reason the coupling circuits are referred to as d.c. restore (or) d.c. reinserter.

​

• Def : “ A clamping circuit is one that takes an input waveform and provides an output i.e., a faithful replica of its shape, but has one edge clamped to the zero voltage reference point.

​

There are two types of clamping circuits.

​

• 1) Negative clamping circuit.
• 2) Positive clamping circuit.

Diode :- Clamper

Positive Clamper

The circuit for a positive clamper is shown in the figure. During the negative half cycle of the input signal, the diode conducts and acts like a short circuit. The output voltage V_o

⇒ 0 volts . The capacitor is charged to the peak value of input voltage V_m. and it behaves like a battery. During the positive half of the input signal, the diode does not conduct and acts as an open circuit. Hence the output voltage V_o ⇒V_m+ V_m This gives a positively clamped

voltage.

V_o ⇒V_m+ V_m = 2

V

m

Negative Clamper

During the positive half cycle the diode conducts and acts like a short circuit. The capacitor charges to peak value of input voltage V_m.

During this interval the output Vo which is taken across the short circuit will be zero During the negative half cycle, the diode is open. The output voltage can be found by applying KVL.

Biased Clamper

CLAMPING CIRCUIT THEOREM

• Therefore the charge acquired by the capacitor during the forward interval

_∴ A_{f =} R_f

A_r R

Consider a square wave input is applied to a clamping circuit under steady state condition

If V_f (t) is the output waveform in the forward direction, then from below figure

the capacitor charging current is

V

_{if =} f

R_f

Therefore the charge acquired by the capacitor during the

forward interval

i dt =

V dt =

T₁ T₁

∫ f

1

R_f

A

f

R_f

∫ f

0 ⁰

…………….. (1)

• Similarly if V_f (t) is the output voltage in the reverse direction, then the current which discharges by the capacitor is

1 ^A_r

T₂ T₂

_∫i_r dt = _R∫ V_r dt = _R

…………….. (2)

T₁ ^T₂

In the steady-state the net charge acquired by the capacitor must be zero.

Therefore from equation (1) & (2) this equation says that

for any input waveform the ratio of the area under the output voltage curve in the forward direction to the reverse direction is equal to the ratio .

Clamping Circuit taking Source and Diode Resistances into account

Practical Clamping circuit

Effect of diode characteristics on clamping voltage

Synchronized Clamping