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FEEDBACK AND STABILITY
THE NEGATIVE-FEEDBACK LOOP
xS = input signal xOUT = AxIN xF = feedback signal xIN = xS xF linear feedback: xF = xOUT =feedback factor ( constant)
xOUT = AxIN = A(xS xF) xOUT = A(xS xOUT)
xIN XOUT A A
xS xIN xOUT
_ Feedback network
Output Signal source
Open loop Closed loop
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xOUT depends upon itself a property intrinsic to the nature of a feedback path
xOUT(1+A) =AxS or A1A
Afb = closed-loop gain (gain with feedback) A>>1
Closed-loop gain, Afb is independent of A in the limit A>>1, depends only on the feedback factor .
This feature is important. It allows Afb to be precisely set regardless of the exact value of A.
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Feedback network is generally made from passive (and easy-to-control) circuit elements and factors that affect A (component variations, temperature, and circuit non-linearity) become much less important to the closed-loop circuit.
Worth the price of reducing gain from AOL to ACL.
Example: Non-inverting op-amp configuration
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GENERAL REQUIRMENTS OF FEEDBACK CIRCUITS
Signals at summing node must be the same type (i.e., all voltages or currents).
The output, xOUT, needs not be of the same signal type as its input. The amplification factor, A, can have dimension units:
Av=Volt/Volt or Ai=Ampere/Ampere Ar=Volt/Ampere or Ag=Ampere/Volt.
Feedback function, , must have units reciprocal to those of A, (i.e., product A is dimensionless -- ensures xF is the same signal type as xS and xIN).
In general, feedback network is made from passive components only and never exceeds unity.
In the feedback loop, xF is subtracted from xS, making the feedback negative.
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If xF is added to xS at the summation node, the feedback becomes positive (oscillator, active filters.)
Negative feedback benefits (desirable in amp. design): Reducing amplifier non-linearity, Improving input and output impedance, Extending amplifier bandwidth, Stabilizing gain, and reducing amplifier sensitivity to transistor
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FOUR TYPES OF NEGATIVE FEEDBACK
Four basic amplifier types
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a. A voltage amplifier with gain Av
b. A current amplifier with gain Ai
c. A transconductance amplifier or voltage-to-current converter. The amplification factor, Ag, or
gm = iOUT/vIN, (A/V or conductance).
d. A transresistance amplifier or current-to-voltage converter. The amplification factor, Ar or
rm, = vOUT/iIN (V/A or resistance).
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The four types of negative feedback In Out Circuit zin zout Converts Ratio Symbol Type of Amplifier
V V VCVS 0 - vo/vi Av Voltage amplifier I V ICVS 0 0 i to v vo/ii rm Trans-resistance amplifier V I VCIS v to i io/vi gm Trans-conductance amplifier I I ICIS 0 - io/ii Ai Current amplifier
vi vo Avvi HIGH
vo riii LOW
gmvi HIGH HIGH
Aivi LOW HIGH
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VOLTAGE-CONTROLLED VOLTAGE SOURCE (VCVS)
High input impedance Low output impedance Stiff voltage source
Closed loop gain: Loop gain:
Error between ideal and exact values:
vin vout + _
A1Gain OLCL +=
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Output voltage: vin=Avout v Negative feedback: Stabilizes voltage gain, Increases input impedance,
Decreases output impedance, Reduces nonlinear distortion of the amplified signal.
a. Gain stability:
The gain is stabilized because depends only on the external resistances (i.e., can be precision resistors).
The gain stability depends on having a low percent error between the ideal and the exact closed-loop voltage gains.
The smaller the percent error, the better the stability. The worst-case error of closed-loop voltage gain occurs when the open-loop
voltage gain AOL is minimum.
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b. Nonlinear distortion:
non-linear distortion will occur with large signals. input/output response becomes non-linear. Nonlinear also produces harmonics of the input signal.
Total harmonic distortion:
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Negative feedback reduces harmonic distortion (closed-loop harmonic distortion):
Quantity 1+AOL has a curative effect. When it is large, it reduces the harmonic distortion to negligible levels, (ex.., high-fidelity sound in audio amplifier system).
Example 19-1, 19-2, 19-3, 19-4 (page 667)
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CURRENT-CONTROLLED VOLTAGE SOURCE (ICVS)
Low input impedance, Low output impedance. Stiff voltage source from a current input. Trans-resistance (rm) (i.e., output voltage is proportional to the current by a
R2 can be selected to have different conversion factors (trans-resistances).
Input and output impedances:
Example: inverting amplifier, 19-5, 19-6 (page 674)
iin vout _
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VOLTAGE-CONTROLLED CURRENT SOURCE (VCIS)
Transconductance, gm, (i.e., 1/R) Both input and output impedances are high Stiff current source.
Input and output impedances:
Example 19-7 (page 677)
vin iout + _
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CURRENT-CONTROLLED CURRENT SOURCE (ICIS)
Low input impedance, High output impedance . Stiff current source. Current gain factor Ai.
Input and output impedances:
Example 19-8 (page 678)
iout _ +
+= 1OL)CL(out R)A1(Z +=
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Negative feedback increases the bandwidth of an amplifier. Because of the roll-off in open-loop voltage gain means less voltage is fed
back, which produces more input voltage as a compensation. Closed-loop cutoff frequency is higher than the open-loop cutoff frequency.
The closed-loop cutoff frequency:
Gain Bandwidth Product
Gain bandwidth product is constant