# Circuit Theory I Opera`onal Amplifier ```Circuit Theory I Opera1onal Ampliﬁer Assistant Professor Suna BOLAT Eastern Mediterranean University Department of Electric and Electronic Eng. Op Amps: Introduc1on •  Op Amp is short form of opera1onal ampliﬁer. •  An op amp is an electronic unit that behaves like a voltage controlled voltage source. •  An opera1onal ampliﬁer has a very high input impedance and a very high gain. 2 Op Amps: Use of Op Amps •  Op amps can be conﬁgured in many diﬀerent ways using resistors and other components. •  Most conﬁgura1ons use feedback. •  An op amp can be designed to perform mathema1cal opera1ons of addi1on, subtrac1on, mul1plica1on, division, diﬀeren1a1on, and integra1on. 3 Op Amps: Applica1ons of Op Amps •  Ampliﬁers provide gains in voltage or current. •  Op amps can convert current to voltage. •  Op amps can provide a buﬀer between two circuits. •  Op amps can be used to implement integrators and diﬀeren1ators. •  Op amps can be used to design ﬁlters (i.e. lowpass and bandpass ﬁlters). 4 Op Amps: Op Amp Symbol A typical op amp: (a) pin conﬁgura1on, (b) circuit symbol. 5 Op Amps: Schema1c diagram of op amp 6 Op Amps: The Op Amp Model InverGng input Output Non-&shy;‐inverGng input The output voltage The diﬀerenGal input voltage A is the open-&shy;‐loop voltage gain. 7 Op Amps: Typical op amp parameters 8 Op Amps: •  Example 5.1: A 741 op amp has an open-&shy;‐loop voltage gain of 2x105, input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed-&shy;‐ loop gain v0/vs. Determine current i when vs = 2 V. Figure 5.6: (a) original circuit, (b) the equivalent circuit. 9 Op Amps: Ideal Op Amp •  An ideal op amp is an ampliﬁer with inﬁnite open-&shy;‐loop gain, inﬁnite input resistance, and zero output resistance. •  To facilitate the understanding of op amp circuits, we will assume ideal op amps. An op amp is ideal if it has the following characteris1cs: 1.  Inﬁnite open-&shy;‐loop gain, A = ∞
2.  Inﬁnite input resistance, Rin=∞
3.  Zero output resistance, Ro=0 10 Op Amps: Ideal Op Amp •  An ideal op amp is an ampliﬁer with inﬁnite open-&shy;‐loop gain, inﬁnite input resistance, and zero output resistance. 1.  Ideal Op Amp Model 1.  Inﬁnite open-&shy;‐loop gain, A = ∞
2.  Inﬁnite input resistance, Rin=∞
3.  Zero output resistance, Ro=0 11 Op Amps: Ideal Op Amp •  Two important characteris1cs of the ideal op amp are: 1.  The currents into both input terminals are zero. This is due to inﬁnite input resistance. An inﬁnite resistance between the input terminals implies that an open circuit exists there and current cannot enter the op amp. 2.  The voltage across the input terminals is equal to zero. An ideal op amp has zero current into its two input terminals and the voltage diﬀerence between the two input terminals is equal to zero. 12 Op Amps: Ideal Op Amp •  Example 5.2: Use the ideal op amp model to calculate the closed-&shy;‐loop gain v0/vs. Find io when vs = 1 V. v2 = v s
⇒ v1 = v2 = vs
KCL at inver1ng terminal (v1): vs − vo vs
+ =0
40
5
9vs = vo
v1 vo KCL at output (vo): io =
vo − vs
vo
+
40 &times;103 20 &times;103
(if vs = 1 V , then vo = 9V) ⇒ io = (0.2 + 0.45) &times;10 −3 = 0.65 mA
13 Op Amps: Inver1ng Ampliﬁer •  Both the input signal and the feedback are applied at the inver1ng terminal of the op amp. Applying KCL at node 1: Noninver1ng terminal is grounded. •
An inver1ng ampliﬁer reverses the polarity of the input signal while amplifying it. 14 Op Amps: Inver1ng Ampliﬁer •  Example 5.3: Refer to the op amp in Figure below. If vi =0.5 V, calculate: (a) the output voltage vo, and (b) the current in the 10-&shy;‐kΩ resistor. (a) (b) 15 Op Amps: Inver1ng Ampliﬁer •  Prac1ce Problem 5.3: Find the output of the op amp circuit shown in Fig. 5.13. Calculate the current through the feedback resistor. 16 Op Amps: •  Example 5.1: A 741 op amp has an open-&shy;‐loop voltage gain of 2x105, input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed-&shy;‐ loop gain v0/vs. Determine current i when vs = 2 V. •  Repeat Ex. 5.1 by using ideal op amp model. 17 Op Amps: Review •  To solve an op amp circuit, we usually apply KCL at one or both of the inputs. •  We then use the proper1es of the ideal model. &sect;  The currents into both input terminals are zero. &sect;  The voltage across the input terminals is equal to zero. •  We solve for the op amp output voltage. 18 Op Amps: Noninver1ng Ampliﬁer •  A noninver1ng ampliﬁer is an op amp circuit designed to provide a posi1ve voltage gain. Apply KCL at inver1ng terminal: (1) (2) Apply eq. (1) into eq (2): Then: 19 Op Amps: Voltage Follower •  A voltage follower (or unity gain ampliﬁer) has the output voltage equal to the input voltage. Voltage follower is a noninver1ng ampliﬁer with: 20 Op Amps: Noninver1ng Ampliﬁer •  Example 5.5: For the op amp circuit below, calculate the output voltage vo . 21 Op Amps: Summing Ampliﬁer (Inver1ng Summer) Apply KCL at node a: 22 Op Amps: Summing Ampliﬁer (Inver1ng Summer) Apply KCL at node a: Note that Then, 23 Op Amps: Summing Ampliﬁer (Inver1ng Summer) •  Example 5.6: Find vo and io in the op amp circuit shown below.
24 Op Amps: Diﬀerence Ampliﬁer Apply KCL at node a: Apply KCL at node b: But 25 Op Amps: Diﬀerence Ampliﬁer •
Diﬀerence ampliﬁer must reject a signal common to the two inputs, the ampliﬁer must have the property that vo=0, when v1= v2. •
This property exists when: •  When this property is sa1sﬁed •  The op amp circuit is a diﬀerence ampliﬁer •  If R2 = R1 and R3 = R4 • The diﬀerence ampliﬁer becomes • A subtractor circuit: 26 Op Amps: Cascaded Op Amp Circuits •
A cascade connec1on is a head-&shy;‐to-&shy;‐tail arrangement of two or more op amp circuits such that the output of one is the input of the next. •  The overall gain of the cascade connec1on is the product of the gains of the individual op amp circuits 27 Op Amps: Cascaded Op Amp Circuits •  Example 5.9: Find v0 and i0 in the circuit below.
28 Op Amps: Cascaded Op Amp Circuits •  Example 5.10: Given that v1 = 1 V and v2 = 2 V, ﬁnd v0 in the circuit below.
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