EC410 Electronic Measurements
Lecture 3: RC Oscillators-Wien Bridge
Oscillator
Lecturer: Azza Kamal
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Questions…?
In this lecture, we are going to answer the following questions…
• What is an oscillator?
• What is the working principle?
• Define the oscillation Conditions
• Types of oscillators
• Wien’s Bridge- Circuit Construction, Derivation & Applications
• example
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Definition
• An oscillator is a circuit that produces a periodic waveform on its output
with only the dc supply voltage as an input.
• A repetitive input signal is not required except to synchronize oscillations
in some applications.
• The output voltage can be either sinusoidal or nonsinusoidal, depending
on the type of oscillator.
• Two major classifications for oscillators are:
1- feedback oscillators
2- relaxation oscillators.
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What are Feedback Oscillators?
• Feedback Oscillator: returns a fraction of the output signal to the input with
no net phase shift.
• Benefits: resulting in a reinforcement of the output signal.
• For a sine wave output: the loop gain is maintained at 1.0 to maintain a
low-distortion output.
What if the gain is > 1?? (the output will be distorted and clipped.)
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Feedback Oscillators (Cont.)
❑Operation Principle of a basic feedback
oscillator that produces a sine wave:
• The amplifier provides just enough gain to
overcome attenuation in the feedback circuit
but may introduce a phase shift in the process
(depending on the type of amplifier).
• The feedback circuit returns a fraction of it to
the amplifier’s input.
• The feedback circuit compensates for any
phase shift introduced by the amplifier.
• The net result is that the input reinforces the
signal to maintain oscillations.
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What are Relaxation Oscillators
• A relaxation oscillator uses an RC timing circuit to generate a
waveform that is generally a square wave or other nonsinusoidal
waveform.
• It uses a Schmitt trigger or other device that changes states to
alternately charge and discharge a capacitor through a resistor.
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Feedback Oscillators: Positive Feedback
• Feedback oscillator operation is based on the principle of positive feedback.
• What is positive feedback?
Positive feedback is characterized by the condition wherein a portion of the output voltage
of an amplifier is fed back to the input with no net phase shift around the loop
Positive Feedback produce Oscillations
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Positive Feedback
What is Oscillation circuit??
• The inphase feedback voltage, 𝑉𝑓 , is
amplified to produce the output
voltage, which in turn produces the
feedback voltage. A loop is created
in which the signal sustains itself
and a continuous sinusoidal output
is produced.
• Note: In some types of amplifiers,
the feedback circuit shifts the phase
180𝑜 and an inverting amplifier is
required to provide another 180𝑜
phase shift so that there is no net
phase shift
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Conditions for Oscillations
Conditions:
1.The phase shift around the feedback loop must be effectively 0.
2. The voltage gain, 𝐴𝑐𝑙 , around the closed feedback loop (loop gain) must equal or greater
than 1 (unity).
• The voltage gain around the closed feedback loop, 𝐴𝑐𝑙 : is the product of the amplifier gain,
𝐴𝑣 , and the attenuation, 𝛽, of the feedback circuit:
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Start-Up Conditions
• For oscillation to begin, the voltage gain around the positive feedback loop must be
greater than 1 so that the amplitude of the output can build up to a desired level.
• The gain must then decrease to 1 to maintain the correct level of output without
distortion.
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Start-Up Conditions
Question: If the oscillator is initially off and there is no output voltage, how does
a feedback signal originate to start the positive feedback buildup process?
• Initially, a small positive feedback voltage develops from thermally produced
broad-band noise in the resistors or other components or from power supply
turn-on transients.
• The feedback circuit permits only a voltage with a frequency equal to the
selected oscillation frequency to appear in phase on the amplifier’s input.
• This initial feedback voltage is amplified and continually reinforced, resulting in
a buildup of the output voltage
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RC Feedback Oscillators
• Three types of feedback oscillators that use RC circuits to produce sinusoidal
outputs are:
• the Wien-bridge oscillator
• the phase-shift oscillator
• the twin-T oscillator.
• Generally, RC feedback oscillators are used for frequencies up to about 1 MHz.
• The Wien-bridge is by far the most widely used type of RC feedback oscillator.
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What is a Wien Bridge Oscillator?
• A Wien-Bridge Oscillator is a type of phase-shift oscillator which is based upon a Wien-Bridge
network.
• It is comprised of four arms connected in a bridge fashion. Here two arms are purely resistive while
the other two arms are a combination of resistors and capacitors.
• In particular, one arm has resistor and capacitor connected in series (R1 and C1) while the other has
them in parallel (R2 and C2).
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Operation of RC Network
• In this circuit, at high frequencies, the reactance of the capacitors C1
and C2 will be much less due to which the voltage V0 will become zero
as R2 will be shorted.
• Next, at low frequencies, the reactance of the capacitors C1 and C2 will
become very high.
• However even in this case, the output voltage V0 will remain at zero
only, as the capacitor C1 would be acting as an open circuit.
• This kind of behavior exhibited by the Wien-Bridge network makes it a
lead-lag circuit in the case of low and high frequencies, respectively.
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Wien Bridge Oscillator Frequency Calculation
• Amidst these two high and low frequencies, there exists a particular
frequency at which the values of the resistance and the capacitive reactance
will become equal to each other, producing the maximum output voltage.
• This frequency is referred to as resonant frequency.
• We obtain the value of the resonant frequency
at the balanced condition of the bridge circuit.
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Construction of Wien’s Bridge
• A null indicator represented by D is linked across the
intersection points of B and D, and an AC voltage source is
connected across the junction AC as shown.
• The deflector is used to keep the bridge in a balanced
condition by ensuring that the voltage values at points B and
D are equal.
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• Impedance Z1 of arm AB is determined as follows:
Arm AB is comprised of resistor R1
connected in parallel with capacitor C1:
• Impedance Z2 of arm AD is determined as follows:
Arm AD is comprised of resistor R2 connected
in series with capacitor C2:
• Impedance Z3 of arm AB is determined as follows:
• Impedance Z4 of arm AB is determined as follows:
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Balanced bridge condition:
Derivation of Frequency of Wien’s Bridge Circuit
Mathematically, the balanced condition of the bridge is obtained by equating the products of
impedance pairs Z1, Z4, and Z2, Z3 as follows:
Substituting the values of impedances Z1, Z2, Z3, and Z4 from equations (1), (2), (3), and (4):
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The next step is to equate the real and imaginary parts of the equation (5):
Equating real parts of the equation (5) on both sides:
Equation (6) shows the relation between resistances R4 and R3.
• If components are selected such that the resistances and
capacitances on arms AB and AD are equal by coupling the
resistances R1 and R2 mechanically as follows
Equating imaginary parts of the equation (5) on both sides:
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Advantages of the Wien’s Bridge
• Simple Circuitry: Wien’s bridge is formed using easily available electronic components namely
resistors and capacitors.
• Cost-effective: Since all the components used to design Wien’s bridge are inexpensive, the cost of
creating the circuit is meager for the manufacturers.
• Quantitative measurements: Wien’s bridge has the capability to measure the frequency and
capacitance of the circuit with high accuracy.
Disadvantages of the Wien’s Bridge
• Limited Frequency Generation: As Wien’s bridge is very sensitive to large frequency values and the
circuit may get destructed at high-frequency values, hence the frequency generated by the bridge is
limited between 100 Hz and 100 kHz.
• High Output distortion: Due to the susceptibility of the Wien’s bridge circuit to large frequency values,
the resultant output signal is highly distorted.
• Not Purely Sinusoidal AC Input Voltage: Due to the presence of harmonic distortions at the input AC
voltage source, the balance condition of the bridge is disrupted.
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Oscillator Output Gain and Phase Shift
• It can be seen that at very low frequencies the phase angle
between the input and output signals is “Positive” (Phase
Advanced), while at very high frequencies the phase angle
becomes “Negative” (Phase Delay).
• In the middle of these two points the circuit is at its resonant
frequency, (ƒr) with the two signals being “in-phase” or 0.
•
We can therefore define this resonant frequency point with
the following expression.
ƒr is the Resonant Frequency in Hertz
R is the Resistance in Ohms
C is the Capacitance in Farads
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How to evaluate the Gain of the feedbk NW (feedback fraction)?
• We said previously that the magnitude of the output
voltage, Vout from the RC network is at its maximum value
and equal to one third (1/3) of the input voltage, Vin to
allow for oscillations to occur.
• But why one third and not some other value??
We have to drive expression for
the feedback fraction β and
obtain the one-third value!
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The Wien-bridge oscillator schematic drawn in two different
but equivalent ways.
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Design Conditions for sustained Oscillation
• The Wien-bridge oscillator circuit can be viewed as a noninverting amplifier configuration with
the input signal fed back from the output through the lead-lag circuit.
• Recall that the voltage divider determines the closed-loop gain of the amplifier.
To achieve a closed loop gain of 3:
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Start-Up Conditions
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Gain Control Approaches:
1-Basic Wien-bridge oscillator with tungsten
lamp for stability.
How??
• The lamp is a resistor with a positive temperature
coefficient, which means it's resistance increases as it gets
warmer.
• The lamp is actually 'powered' by the output of the oscillator,
so the larger the amplitude of the oscillation the warmer the
lamp gets and the greater it's resistance becomes.
• Initially, the feedback resistor, 𝑅𝑓 , is set to a resistance that is
slightly more than twice the lamp’s cold resistance.
• This means the gain of the non-inverting amplifier will be > 3
as required for startup.
• As current warms the lamp, its resistance increases until the
lamp resistance is exactly one-half 𝑅𝑓 , producing a gain of
exactly 3 and the output is stable
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Gain Control Approaches (Cont.):
2- JFET as a voltage-controlled resistor in a negative
feedback path.
• A JFET operating with a small or zero 𝑉𝐷𝑆 is operating in the ohmic
region. As the gate voltage increases, the drain-source resistance
increases.
• The gain of the op-amp is controlled by the components shown in the
shaded box, which include the JFET.
• The JFET’s drain-source resistance depends on the gate voltage.
• With no output signal, the gate is at zero volts, causing the
drain-source resistance to be at the minimum.
• With this condition, the loop gain is greater than 1.
• Oscillations begin and rapidly build to a large output signal.
• Negative excursions of the output signal forward-bias D1,
causing capacitor C3 to charge to a negative voltage.
• This voltage increases the drain-source resistance of the JFET and
reduces the gain (and hence the output).
Ohmic Region:
• The ohmic region of JFET is a region at which
drain current shows linear behavior for
variation in the drain-source voltage.
•
This behavior is like to the ohms law so called
ohmic region.
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Applications of Wien's Bridge :
• The capacitance is measured if the supply frequency is known.
• The frequency used in capacitance measurement is generally in the audio
range i.e., 20 Hz to 20 kHz because at higher frequency the circuit gets
damaged due to the effects of stray capacitance and loss in the capacitor.
• It can also be used as a frequency determining element in audio and radio
frequency oscillators, and harmonic distortion analyzer.
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