Positive feedback: Oscillators

Basics of Oscillator
Prof. Yeshudas Muttu
Assistant Professor
Department of Electronics & Telecommunication Engineering
Don Bosco College of Engineering, Goa

Stability of Feedback Amplifier
 In NFA, Gain A & phase shift of the amplifier changes with frequency.
i.e. at low & high frequencies, Gain decreases.
 Also, Phase shift changes at higher frequencies, that adds some
feedback signal to the input.This results in +ve feedback.
 Due to this +ve feedback, the amplifier breaks out into oscillations.
2 Prof.Yeshudas Muttu

 The amplifier will be useless if suddenly it breaks out into oscillations.
Hence Feedback amplifier should be properly designed in such a way
that the circuit is stable at all frequencies.
 For System to be stable, all the poles & zeros of the transfer function
must lie on the Left half of the complex plane.

Nyquist Criterion
 To check the stability of the system, Nyquist diagram is used.
 It plots gain & phase shift as a function of frequency on the complex
plane.
 We know that Aβ is a complex number & a function of frequency.
 For the values of Aβ, points in the complex plane are obtained
corresponding to the values of frequency from −∞ to + ∞
 The locus of all these points forms a closed curve.
 Nyquist criterion for stability states that an amplifier is unstable if
the Nyquist curve encloses the -1 + j0 point & the amplifier is stable
if the Nyquist curve does not encloses the same point.

 The Nyquist criterion in complex plane can also represent +ve & -ve
feedback.
 |1+Aβ| = 1 represents unity circle, with center -1+j0 point.
 If |1+Aβ| >1 i.e. if Aβ extends outside the unity circle, the feedback is
negative.
 If |1+Aβ| <1 i.e. if Aβ lies within the unity circle, the feedback is positive.
 The amplifier is stable if locus Aβ does not enclose the point -1+j0. i.e.
|1+Aβ| >1 & the feedback is negative for all frequencies.

Gain Margin & Phase Margin
 With Nyquist Criterion, we can say
that feedback amplifier is stable if the
loop gain, Aβ < 1 (0 dB) when phase
angle is 180o.
 From Bode plots, we can find some
margins of stability to indicate how
close to instability the system is.
 Gain Margin  Value of |Aβ| in dB at
the frequency at which phase angle of
Aβ is 180o.
 If Gain Margin is negative, the amplifier is unstable. If positive, the amplifier
is stable.
 Phase Margin  180o – angle(|Aβ|) at which (|Aβ| is unity (0 dB)

Gain Margin & Phase Margin

Oscillator
 An oscillator is the basic element of all ac sources and
generates sinusoidal signals of known frequency and amplitude.
 Oscillator is said to “generate” a sinusoidal signal, but it doesn’t
create energy.
 It only acts as an energy converter. It converts current from dc
supply into ac current of desired frequency. (reverse function as
that of a rectifier).
 But we consider oscillator circuits as providing ac voltage signal.

Amplifier
 Amplifier strengthens the
input signal without any
change in its waveform and
frequency.
 Additional power required
comes from the dc source.
 Amplifier is energy converter
that draws energy from dc
supply and converts it into ac
energy at signal frequency.
 The energy conversion process
is controlled by the input signal.
Oscillator
 Oscillator converts current
from dc supply into ac current
of desired frequency.
 It doesn’t require any external
signal either to start or
maintain the process of energy
conversion.
 The energy conversion is
controlled by oscillator circuit
itself.

Classification of Oscillators
10
1. Based on the type of functions performed.
a) Signal generator/test oscillator
b) Standard signal generator/ function generator
II. Based on the fundamental mechanism.
a) Negative Resistance Oscillators
b) Feedback Oscillators
III. Based on the frequency generated.
a) Audio Frequency Oscillator (AFO): Up to 20 KHz
b) Radio Frequency Oscillator (RFO): 20 KHz – 30 MHz
c)Very High Frequency Oscillator (VHF): 30 MHz – 300 MHz
d) Ultra High Frequency Oscillator (UHF): 300 MHz – 3 GHz
e) Microwave Frequency Oscillator:Above 3 GHz
IV. Based on the type of circuit used.
a) LCTuned Oscillator
b) RC Phase Shift Oscillator
Prof.Yeshudas Muttu

Harmonic Oscillators
 In harmonic oscillators, flow of
energy is in one direction
(from active components to
passive components).
 The frequency of oscillation is
determined by the feedback
path.
 Can develop low-distortion
sinusoidal output waveforms
Relaxation Oscillators
 In relaxation oscillators, the
energy is exchanged
between active and passive
component.
 The frequency of oscillation
is determined by charging
and discharging time
constants during transfer of
energy.
 Can generate only non-
sinusoidal waveforms such as
sawtooth, square or
triangular.

Barkhausen’s Criterion
Prof.Yeshudas Muttu12
 Also, feedback must be positive. i.e. the voltage derived from the
output using feedback network must be in phase withVi.
 Hence, feedback network must introduce a phase shift of 180o
while giving it back from output to input. This ensures positive
feedback.
 When input is applied to the amplifier,
o/p is 180o out of phase with respect
to the input.
 But now, Vi needs to be derived from
its output through the feedback
network.

………(1)
………(2)

 In reality, no input signal is needed to start oscillations.
 Practically, Aβ is made > 1 to start the oscillations.
 Later the circuit adjusts itself to get Aβ = 1, resulting into self
sustained oscillations

Starting Voltage in Oscillators
 No external input is required in case of oscillators.
 The oscillator o/p supplies its own input under proper conditions.
If no input is required, how oscillator starts?
From where does the starting voltage come?
 Every resistance has some free electrons. With normal room
temperature, they start moving randomly in various directions.

Starting Voltage in Oscillators
 Such movement of free es- generate a voltage called noise voltage
across the resistance & these voltages gets amplified.
 To do so, Aβ is kept > 1 at start. Such amplified v/g appears at the o/p
terminals.
 The part of o/p is sufficient to drive the i/p of the amplifier circuit.
 The circuit then adjusts itself to get Aβ = 1 & with 360o phase shift, we
get sustained oscillations.

Basic block diagram of an Oscillator
19
Can be LC, RC, crystal
depending upon the
frequency & shape of the
waveform required
Receives dc power &
converts it into ac for
the supply of tank
circuit
Supplies part of output to
the tank circuit in correct
phase to ensure positive
feedback.
• Oscillations from the tank circuit are
applied to amplifier which amplifies
these oscillations.
• O/p of amplifier is fed back to tank
circuit to make up for losses.
Prof.Yeshudas Muttu

LC oscillators
 Oscillators which use L & C (Inductance- Capacitance circuits
as their tank or oscillatory circuits are called L-C oscillators.
 Circuit using L & C is called a Tank Circuit/Oscillatory Circuit.
It is also termed as resonant circuit/ tuned circuit.
 LC oscillators are very popular for generating high-frequency
outputs (eg. 10 KHz to 100MHz).
 LC oscillators used are Tuned collector oscillators, Colpitt’s
oscillators, Hartley oscillators, Clapp oscillator, Crystal
oscillators, etc.

Operation of LC Tank Circuit
• It consists of L & C components
connected in parallel.
• Let the Capacitor be initially charged by a
DC source with the polarities as shown in
the figure.
• When the capacitor gets charged, it
stores the electrostatic energy.
• When such charged capacitor is
connected across the inductor, the
capacitor starts discharging through it,
that leads in current flow.

22
• Due to such current flow, magnetic field gets
setup around the inductor.
• Hence inductor starts storing energy.
• When the capacitor is fully discharged,
maximum current flows thru’ the circuit.
• i.e. entire electrostatic energy gets stored as
magnetic energy in the inductor.
• Now, Magnetic energy around the inductor starts
collapsing and produces the counter EMF.
• As per the Lenz’s law, this counter EMF produces
the current which begin to charge the capacitor
with opposite polarity by making its upper plate
negative and lower plate positive.
Prof.Yeshudas Muttu

 After some time, the capacitor gets fully
charged with opposite polarities,
converting entire magnetic energy back
into electrostatic energy.
 Capacitor again starts discharging thru L,
but the direction of current is now
opposite to that of previous circuit.
 Again, electrostatic energy is converted to
magnetic energy.
 When the capacitor is fully discharged, magnetic field starts collapsing,
charging the capacitor again in opposite direction.
 Thus capacitor charges with alternate polarities & discharges producing
alternating current in the tank circuit, also known as oscillatory current.

 But every time when the energy is transferred from C to L & L to
C, losses occur.
 Hence, amplitude of oscillating current keeps on decreasing every
time when the energy transfer takes place.
 This results in exponentially decaying oscillations, known as damped
oscillations, that eventually dies off after some time.
 In LC Oscillators, transistor
supplies for this loss in energy
at proper times.
 The care of proper polarity is
taken by the feedback
network.
Results using LC Tank Circuit

Results using LC Tank Circuit
 Thus, LC tank circuit along with transistor amplifier forms LC
Oscillator circuit.
 As it supplies the energy which had got lost, the oscillations gets
maintained.
 These oscillations are called Sustained/undamped oscillations.
 The frequency of oscillations generated by LC tank circuit depends
on the values of L & C given by:

General form of LC Oscillator
 Z1, Z2 acts as AC voltage divider for output voltage &
feedback signal.
 Hence voltage across Z2 is feedback signal.
Amplifier Any Active devices like BJT,
FET, Op-amps, etc can be
used.
Z1,
Z2,
Z3
Reactive elements (L & C)
Forms the feedback tank
circuit
decides frequency of
oscillation

Equivalent circuit for the
General form of LC Oscillator
Assumptions:
1. hre of transistor is negligibly small & hence feedback
source hreVout is negligible.
2. hoe of the transistor is very small. i.e. the output
resistance 1/hoe is very large, hence omitted.

To determine Load impedance between output terminals 1 & 2
ZL
’

To determine Load impedance between output terminals 1 & 2

To determine A, Vout & Vf
……..(2)
……..(1)
……..(3)

To determine β & apply Barkhausen’s
criteria
……..(4)

To determine general equation for Oscillator
……..(5)

COLPITT’S OSCILLATOR
33
• Construction
• Working
• Analysis
Prof.Yeshudas Muttu

34
Colpitt’s oscillator
• up to 100MHz.
• Single stage inverting
amplifier
• LC phase shift network
Series capacitors C1 and C2
form the potential divider that
provides required voltage.
VC2 provides the regenerative
feedback for sustained
oscillations.
RE || CE along with
R1 and R2 provides
the stabilized
Voltage divider bias.
Radio frequency choke
(RFC)
• allows an easy flow of
direct current
• offers very high Z to
the high frequency
currents.
• Energy across
RFC is capacitively
coupled to tank
circuit via CC2.
• CC2 doesn’t allow
dc currents to go
to tank circuit.
Construction Prof.Yeshudas Muttu

35
• The output of LC network is
coupled from the junction of L
and C2 to the base through
coupling capacitor Cc1
• CC1 blocks dc but provides
path to ac.
• Transistor provides
a phase shift of 180°.
• LC feedback network
provides another
phase shift of 180°.
Construction Prof.Yeshudas Muttu
• Total phase shift of 360°
is obtained.
(essential condition for oscillations)
 Vout is derived
from a 2o winding
L’ coupled to the L.
 The frequency is
determined by the
tank circuit.
 It is varied by
gang tuning C1
and C2.
 i.e. values of both
capacitors are
varied
simultaneously,
maintaining the
ratio of the two
capacitances same.

How are oscillations generated?
 When VCC is switched ON, C1 and C2
gets charged.
 Later, they discharge through the coil L,
setting up oscillations of frequency,
f =
𝟏
𝟐𝝅
𝟏
𝑳𝑪 𝟏
+
𝟏
𝑳𝑪 𝟐
 The oscillations across C2 are applied to
the BE junction that appear in the
amplified form at the collector circuit,
whose frequency is the same frequency
as that of the oscillatory circuit.

How are oscillations generated?
 This amplifier output at the collector
circuit is supplied to the tank circuit in
order to meet losses.
 Thus the tank circuit is getting energy
continuously from the collector circuit
to make up for the losses occurring in
it and, therefore, ensures undamped
oscillations.
 The energy supplied to the tank circuit
is of correct phase and ‘Aβ’ equals
unity so that oscillations are sustained
in the circuit.

Mathematical Analysis

40
Rearranging the terms,
………………(1)
Prof.Yeshudas Muttu

41
………………(2)
As for other oscillator circuits,
Loop gain must be greater than unity to
ensure that circuit oscillates
Prof.Yeshudas Muttu

Clapp’s Oscillator
 Clapp’s oscillator is a refinement of the Colpitt’s oscillator.
 Single inductor found in Colpitt’s oscillator is replaced by a
series L-C combination.
 Addition of C3 in series with L
improves the frequency stability and
eliminates the effect of transistor
parameters on the circuit operation.
 As the circulating tank current
flows through C1, C2 and C3 in
series, the equivalent capacitance is

 C1 & C2 are kept fixed while C3 is used for tuning purpose.
 C3 is much smaller than C1 & C2. Hence equivalent capacitance is
approximately equal to C3.
 Hence, Frequency of Oscillation is given as:
 However, care needs to be taken to choose C3.
 If C3 is made too small, L-C branch will not have a net inductive
reactance & under this condition, circuit will refuse to oscillate.

Why is Clapp’s oscillator preferred
over a Colpitt’s oscillator?
 In a Colpitt’s oscillator, the resonant frequency is affected by
the transistor and stray capacitances because the capacitors C1
and C2 are shunted by the transistor and stray capacitances
and so their values are altered.
 But in a Clapp’s oscillator, the transistor and stray
capacitances will have no effect on the capacitor C3 , so
oscillation frequency is stable and accurate.
 For this reason, Clapp oscillator preferred over a Colpitt’s
oscillator.

Numerical

Problems for Practice

Hartley Oscillator
Assistant Professor

49
Construction & Working
Hartley’s oscillator
• Local oscillator in radio
receivers
• Similar to Colpitt’s
oscillator circuit
The Phase shift
network consists of
two inductors L1 and
L2 and a capacitor C
• However, because of
direct connection,
junction L1 and L2 cannot
be directly grounded.
• Instead another
capacitor CL is used.
Output of amplifier is
applied to L1 and voltage
across inductor L2 from
the feedback voltage.
Coil L1 is inductively
coupled and L2, the
combination functions
as an auto-transformer.
• The operation of the circuit is
similar to that of the Colpitt’s
oscillator circuit.
Prof.Yeshudas Muttu

50
 L1 & L2 are wound on the same core. Hence, there exists
mutual inductance ‘M’ which will increase net effective
Inductance ‘L’ given by:
L = L1 + L2 + 2M
 Resonant /Frequency of Oscillation is given by:
Construction & Working
Prof.Yeshudas Muttu

Rearranging the terms,
………………(1)
………………(2)

54
As for other oscillator circuits,
Loop gain must be greater than unity to
ensure that circuit oscillates
Prof.Yeshudas Muttu

Tuned Collector Oscillator
55
It is named so because the
tuned circuit is connected
to the collector.
• The tuned circuit
consists of C and
transformer 1o coil L
• determines the
frequency of oscillation.
• L forms the load
impedance
R1 R2, and RE form the
dc biasing circuit of
the transistor.
C1 and CE are bypass
capacitors for R2 and RE
respectively
Construction:
• C1 provides ac
ground for the
transformer 2o.
• If absent, Vf will not
be directly fed to the
base, but part of it will
get dropped across R2
Vout across the tuned
circuit is inductively
coupled to the base
circuit through L1.
Vf appears across the BE
junction, as the junction
point of resistors R1 and R2
is at ac ground due to
bypass capacitor Cl .
Prof.Yeshudas Muttu

56
 A phase shift of 180° is provided by the
transistor amplifier, as it is connected in
CE configuration.
 Another phase shift of 180° is provided by
the transformer.
 Thus a total phase shift of 360 °appears
between the input and output voltages
 i.e. There is a positive feedback between
the input and output voltages.
Construction:
Prof.Yeshudas Muttu

57
Working:
 When VCC is switched on, a transient
current is caused in the tuned L-C circuit.
It is due to increase of collector current
to its quiescent value.
 This transient current initiates natural
oscillations in the tank circuit.
 These natural oscillations induce some
voltage into L1 by mutual induction which
causes corresponding variations in base
current.
 These variations in base current are
amplified β times and appear in the
collector circuit.
Prof.Yeshudas Muttu

58
 A part of this amplified energy is used to
meet the losses that occur in the tank
circuit and the rest is radiated out in the
form of electromagnetic waves.
 The turns ratio of L and L1 is determined
by the total losses.
 Higher the turn ratio, lesser is the
feedback voltage applied and vice-versa.
 The frequency of oscillation i.e. The
frequency at which Barkhausen’s criterion
is satisfied differs from the resonant
frequency of the tuned circuit due to
loading of the transformer 2o.
Prof.Yeshudas Muttu

59
Practice 1: In Hartley Oscillator, the tank circuit has the capacitance of 100 pF.
The value of Inductance between the collector & tapping point is 30 mH & the
value of inductance between the tapping point & the transistor base is 10 nH.
Determine the frequency of oscillations. Neglect Mutual inductance.
Practice 2: Determine the oscillation frequency of a transistor Hartley
oscillator with circuit values L1 = 1 mH, L2 = 100 µH, M = 50 µH & C = 100 pF.
Practice 3: The tuned collector oscillator makes use of an L-C tuned circuit
with L = 29.3µH & C = 450 pF. Determine the oscillation Frequency.
Practice 4: A tuned collector oscillator has a fixed inductance of 100µH & has
to be tunable over the frequency band of 100 KHz to 1500 KHz. Find the range
ofVariable capacitor to be used.
Prof.Yeshudas Muttu

Audio Oscillators
Assistant Professor

Introduction
61
 LC oscillators can generate higher frequencies, but cannot be
used to generate low frequencies as they become expensive.
 RC Oscillators are used to generate audio frequencies as they
provide good frequency stability & correct waveform.
 With IC technology, its easy to use RC oscillators as
inductance of larger values are difficult to make.
 Two types of RC Oscillators are:
1. RC Phase Shift Oscillator
2. Wien Bridge Oscillator
Prof.Yeshudas Muttu

Basic Principle of RC Oscillators
62
 For +ve feedback at one particular frequency, an inverting amplifier
may be used with the feedback network that causes phase shift of
180o at desired frequency of oscillation.
 The 180o phase shift in the feedback signal can be obtained by using
RC sections.
 For this, R & C should be selected in such a way that, it produces
180o phase shift at desired frequency of oscillation.
Prof.Yeshudas Muttu

RC Phase Shift Oscillator
63
 Here, RC network is used in feedback path.
 We know that, feedback network should produce phase shift of
180o so that total phase shift in the loop is 360o.
 Thus if one RC network produces 60o, then total phase shift due to
feedback will be 60o x 3 = 180o.
Prof.Yeshudas Muttu

64
Construction
The value of R’ should
be such that, when
added with hie, it is
equal to R. i.e.
R’ + hie = R
Prof.Yeshudas Muttu
Here, feedback signal is
coupled through resistor
R’ in series with amplifier
input resistance, hie.
R1, R2, RE, CE together
provides voltage divider bias,
temperature stability to the
transistor & ac degeneration.
Oscillator output voltage
is capacitively coupled to
the load thru’ Cc.
The output feedback
network is loaded with
small input resistance.
i.e. hie of the transistor.
Rc provides control over
output voltage.

65
Working
Prof.Yeshudas Muttu
RC phase shift network
helps in determining
frequency of oscillations.
Noise inherent in the
transistor/ minor variations
in dc supply leads to
random variation in base
current that sets the circuit
into oscillations.
RC network produces
phase shift of 180o
between o/p & i/p
voltages.
CE amplifier produces
phase reversal of 180o.
Hence total phase
shift in the network is
360o.
This variation in IB is
amplified by the
transistor in the collector
circuit which is than fed
to RC feedback network.
Since resistance is also
involved in his, it tends
to attenuate the
output voltage,

Assumptions:
1. hre of transistor is negligibly small & hence feedback source
hreVout is negligible.
2. hoe of the transistor is very small. i.e. the output resistance
1/hoe is very large, hence omitted.

 Applying KVL in all 3 loops,
………………(1)
………………(2)
………………(3)

68
 Solving equations 1, 2 & 3, determinants of coefficients of currents
equals zero.
………………(4)
Prof.Yeshudas Muttu

………………(5)
………………(6)

70
For Loop gain to be greater than unity, the requirement of current gain of the
transistor is:
Prof.Yeshudas Muttu
………………(7) ………………(8)

Wien Bridge Oscillator
73
 It employs two transistors each producing phase shift of 180o, thus
producing total phase shift of 360o.
 It uses two-stage amplifier with an RC bridge circuit.
Prof.Yeshudas Muttu

Construction – Lead lag Explanation
74
 The phase shift across the network lags with increasing the frequency &
leads with decreasing frequency.
 By adding Wien bridge feedback network,
the oscillator becomes more sensitive
to a signal of one particular frequency.
 R-C bridge circuit/ Wien bridge is a lead – lag network. (R1-C1 & R2-C2)
Prof.Yeshudas Muttu

Construction – Frequency Stability Explanation
75
 At this frequency, Wien bridge is said to be balanced
for which phase shift is 0o.
 Hence, Use of Wien bridge improves frequency
stability.
 If Wien bridge is not used & Q2 o/p is fed back
to Q1 for necessary oscillations, Q1 will amplify
signals over wide range of frequencies.
 This increases the network frequency instability.
Prof.Yeshudas Muttu

76
Z1 = 𝑅1 +
1
𝑗𝜔𝐶1
= 𝑅1 −
𝑗
𝜔𝐶1
Z2 = R2 || C2
= R2 ||
1
𝑗𝜔𝐶2
=
𝑅2×
1
𝑗𝜔𝐶2
𝑅2+
1
𝑗𝜔𝐶2
=
𝑅2
1+𝑗𝜔𝑅2 𝐶2
Z4 = R4
Z3 = R3
Prof.Yeshudas Muttu

77
 For Bridge balanced condition,
Z1Z4 = Z2Z3
Prof.Yeshudas Muttu
…………..(1)

…………..(2)
…………..(3)
…………..(5)
…………..(4)

Construction: Feedback & Gain Stability
79
 2 – stage amplifier consists of Q1 & Q2. Q1 serves as an oscillator &
amplifier whereas Q2 serves as an inverter to provide another phase
shift of 180o.
 Circuit uses +ve & -ve feedback. +ve feedback is thru’ R1-C1, R2-C2 to Q1.
–ve feedback is thru’ voltage divider R3 & R4 to the emitter of Q1.
Prof.Yeshudas Muttu

80
𝑨 = 𝟏 +
𝑹 𝟑
𝑹 𝟒
= 𝟏 + 𝟐
= 𝟑
𝑨 = 𝟏 +
𝑹 𝒇
𝑹 𝟏
Prof.Yeshudas Muttu

Construction: Importance of –ve feedback
81
 2 – stage amplifier provides gain, much larger than 3. To reduce the
gain, negative feedback is used without bypassing R4.
 This ensures gain stability that can control the output amplitude &
also it reduces distortion.
 Amplitude stability can be improved by using non-linear R4.(Eg: lamp)
Prof.Yeshudas Muttu

Construction: More amplitude stability
82
 Loop gain depends on the amplitude of oscillations.
 Increase in the amplitude of oscillations increases the current thru’
non-linear R4.
 This increases the value of non-linear R4 which increases the
amount of negative feedback applied.
 This reduces the loop gain & hence amplitude gets reduced &
controlled.
Prof.Yeshudas Muttu

Working
83
 Noise inherent in the transistor/ minor variations in dc supply leads to random
variation in IB of Q1 that sets the circuit into oscillations.
 This variation in IB is amplified by the transistor in the collector circuit of Q1 with
phase shift of 180o.
 The Q1 collector o/p is fed to the base of Q2 thru’ C4.
 The signal is further amplifier & another 180o phase shifted. Having inverted twice,
o/p signal will be in-phase with i/p signal at base of Q1.
Prof.Yeshudas Muttu

Working
84
 Part of o/p of Q2 is fed back to the bridge at points A & C. A part of this is applied
to R4 where it produces negative feedback(degenerative effect).
 A part of feedback signal is applied across base bias resistor R2 produces positive
feedback(regenerative effect).
 To obtain sustained oscillations, regenerative effect is made slightly greater than
degenerative effect.
Prof.Yeshudas Muttu

Selection of Oscillator
86
1. Frequency range
2. Power/ Voltage requirements
3. Amplitude & Frequency stability
4. Waveform distortion
5. Output Impedance – for maximum power transfer.
Prof.Yeshudas Muttu

References
88
 Electronic Devices & Circuits – J.B. Gupta
 Analog Electronic Circuits – A.P. Godse, U.A. Bakshi
 Electronic Devices & Circuits – K. Lal Kishore
 https://www.youtube.com/watch?v=4Yyu5RRCFYw
 https://www.sciencedirect.com/topics/engineering/phase-
crossover-frequency
 http://www.schoolphysics.co.uk/
Prof.Yeshudas Muttu

Positive feedback: Oscillators

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