Chapter 11 Operational Amplifiers and Applications. Chapter Goals. Understand the “magic” of negative feedback and the characteristics of ideal op amps. Understand the conditions for non-ideal op amp behavior so they can be avoided in circuit design.
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A = open-circuit voltage gain
vid = (v+-v-) = differential input signal voltage
Rid= amplifier input resistance
Ro= amplifier output resistance
The signal developed at the amplifier output is in phase with the voltage applied at the + input (non-inverting) terminal and 180° out of phase with that applied at the - input (inverting) terminal.
But is= i2 and v- = 0 (since vid= v+ - v-= 0)
Rout is found by applying a test current (or voltage) source to the amplifier output and determining the voltage (or current) after turning off all independent sources. Hence, vs = 0
Since v- = 0, i1=0. Therefore vx = 0 irrespective of the value of ix .
and Av = -100
A minus sign is added since the amplifier is inverting.
But vid =0
Rout is found by applying a test current source to the amplifier output after setting vs = 0. It is identical to the output resistance of the inverting amplifier i.e. Rout = 0.
Ab is called loop gain.
For Ab >>1,
This is the “ideal” voltage gain of the amplifier. If Ab is not >>1, there will be “Gain Error”.
is called the feedback factor.
GE = (ideal gain) - (actual gain)
For the non-inverting amplifier,
Note: R1 and R2 aren’t designed to compensate for the finite open-loop gain of the amplifier.
Practical op amps have limited output voltage and current ranges.
Voltage: Usually limited to a few volts less than power supply span.
Current: Limited by additional circuits (to limit power dissipation or protect against accidental short circuits).
The current limit is frequently specified in terms of the minimum load resistance that the amplifier can drive with a given output voltage swing. Eg:
For the inverting amplifier,
Non-inverting Amplifier Circuits
Since i-=0, i3= i1 + i2,
Since the negative amplifier input is at virtual ground,
Since v-= v+
For R2= R1
Here Adm is called the “differential mode voltage gain” of the difference amplifier.
A(or Adm) = differential-mode gain
Acm = common-mode gain
vid = differential-mode input voltage
vic = common-mode input voltage
A real amplifier responds to signal common to both inputs, called the common-mode input voltage (vic). In general,
An ideal amplifier has Acm = 0, but for a real amplifier,
The output error introduced by finite CMRR is 25% of the expected ideal output.
Combines 2 non-inverting amplifiers with the difference amplifier to provide higher gain and higher input resistance.
Ideal input resistance is infinite because input current to both op amps is zero. The CMRR is determined only by Op Amp 3.
Use a phasor approach to gain analysis of this inverting amplifier. Let s = jw.
fcis called the high frequency “cutoff” of
the low-pass filter.
Input resistance is controlled by R1 and voltage gain is set by R2 / R1.
The cutoff frequency is then set by C.
The closest standard capacitor value of 160 pF lowers cutoff frequency to 1.99 kHz.
Since Rout= 0
Rin= RinA andRout= RoutC = 0
The ideal gain for the voltage follower is unity. The gain error here is:
Since, both A and CMRR are normally >>1,
Since A ~ 106 and CMRR ~ 104 at low to moderate frequency, the gain error is quite small and is, in fact, usually negligible.