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**EE174 – SJSU Lecture #1 Tan Nguyen**

Op-Amp EE174 – SJSU Lecture #1 Tan Nguyen

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**Operational Amplifier**

Introduction Brief of History Fundamentals of Op-Amps Applications

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Introduction Operational Amplifier (Op-Amp) is an active circuit element design to perform mathematic operations. Op-Amp is a low cost integrating circuit consisting of transistors, resistors and capacitors. Op-Amp amplify an input signal produces an output voltage equal to the difference between the two input terminals multiplied by the gain A

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**Op-Amps are commonly used for both linear and nonlinear applications:**

Inverting/Non-inverting Amplifiers Variable Gains Amplifiers Summers Integrators/Differentiators Filters (High, Low, Band Pass and Notch Filters) Schmitt trigger Comparators A/D converters

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Brief History Vacuum Tubes Op-Amp (use ±300 to ±100V) built in 1930’s-1940’s Solid State Discrete Op-Amps (use ±15 to ±10V) 1960’s Integrated Circuit Op-Amp (µA702 in 1963 and µA741 in 1968)

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**The Equivalent Circuit of the Op-Amp**

vd = v+ - v- vo = Avd = A(v+ – v-) Note: v+ = v2, v- = v1 Parameters of Typical Range vs Ideal Values of the Op Amp

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The Ideal Op-Amp V- V+ 1) The input impedance Ri is infinite - i.e. no current flows into either input. 2) The output impedance Ro is zero - i.e. the op-amp can drive any load impedance to any voltage. 3) The open-loop gain (A) is infinite. 4) The bandwidth is infinite. 5) The output voltage is zero when the input voltage difference is zero.

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**Op-Amp Gain Open loop gain:**

This form of gain is measured when no feedback is applied to the op amp. Figures are often quoted in the op amp datasheets in terms of volts per millivolt, V/mV. Closed loop gain: This form of gain is measured when the feedback loop is operation, i.e. a closed loop.

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Op-Amp Gain The Voltage Gain (AV) of the operational amplifier can be found using the following formula: and in Decibels or (dB) is given as:

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Closed Loop Gain Example: A closed-loop gain of A = 10 or 20 log (10) = 20dB.

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**BANDWIDTH AND FREQUENCY**

The bandwidth (BW) of an amplifier is the range of frequencies, from lowest to highest, over which the amplifier delivers sufficient gain. The meaning of "sufficient" depends on your application, but one common meaning is when the gain (20 Log Av) has dropped by 3dB. ". How much bandwidth does an audio amplifier need? In a telephone circuit, 300 Hz to 3300 Hz is adequate bandwidth. In high-fidelity audio, 20 Hz to 20 kHz would be required. In some applications, 100 kHz is considered to be an "audio" frequency.

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Feedback vs bandwidth Applying feedback will reduce the gain but increase the bandwidth.

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Gain Bandwidth (GBW) The GBW of a given amplifier is a constant. If you set the amplifier to a gain of A (ratio, not dB), then the bandwidth is given by: BW = GBW / A For example, suppose the unity GBW is 1,000,000. At a gain of 10, the amplifier will have a bandwidth of 100,000 Hertz. At a gain of 100, the amplifier will have a bandwidth of only 10,000 Hertz.

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**An Operational Amplifiers Bandwidth**

Example: Find BW for the gain of 37dB. Using the formula 20 log (A), we can calculate the bandwidth of the amplifier as: 37 = 20 log A therefore, A = anti-log (37 ÷ 20) = 70.8 GBW ÷ A = Bandwidth, therefore, 1,000,000 ÷ 70.8 = 14,124Hz, or 14kHz

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Slew Rate The slew rate of an op amp or any amplifier circuit is the rate of change in the output voltage caused by a step change on the input.

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**Slew rate calculation & formula**

Where slew rate is measured in volts / second, although actual measurements are often given in v/µs f = the highest signal frequency, Hz V = the maximum peak voltage of the signal. As an example, take the scenario where an op amp is required to amplify a signal with a peak amplitude of 5 volts at a frequency of 25kHz. An op amp with a slew rate of at least 2 π x x 5 = 785,000V/s or 0.785V/µs would be required

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Op Amp Offset Null The offset null capability is used to reduce small DC offsets that can be amplified. These can be important in DC amplifiers where these small voltages can then become significant where large gains are required. This input offset voltage is small and arises from mismatches in the differential input stage of the op amp chip. These small offsets are caused by a variety of unavoidable issues within the manufacture of the op amp. They include aspects including mismatched transistor pairs, collector currents, current-gain betas (β), collector or emitter resistors, etc..

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To remove or null the offset, many op-amp chips provide two pins that enable this to be done. Using the offset null adjustment requires a potentiometer with its wiper connected to the negative supply with some op amps or to 0 V with othersVR1 is typical 10 KΩ to 100 KΩ.

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**The Voltage Follower VOUT = A/(A+1) V+ VOUT = V+= VIN VOUT = VIN**

VOUT = A(V+ - V-) VOUT = A/(A+1) V+ VOUT = V+= VIN V+ V- VOUT = VIN Voltage followers are used to buffer or isolate a low impedance load from a voltage source.

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**The Inverting Op Amp vOUT = - (R2 /R1)vin VOUT = A(0-V-) thus**

The V- terminal is referred to as a "virtual ground“ due to negative feedback. VOUT = A(0-V-) thus Apply KCL at node A: i1 = i2 (vin – v-)/R1= (v- – vOUT)/R2 Since v-= v+ = 0, vi /R1 = - vOUT/R2 or vOUT = - (R2 /R1)vin

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**The Non-Inverting Amp vout= (1 + R2 /R1)vin**

v- = v+ = vi n vi n = R1 i1 Since no current flows into either of the Op-Amp inputs i1 = i2 Vout = R1 i1 + R2 i2 = Vin + R2 Vin/R1 vout= (1 + R2 /R1)vin

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**The Summing Amp i = i1 + i2 + i3 i1 = (v1 – va)/R1 i2 = (v2 – va)/R2**

i3 = (v3 – va)/R3 i = (va – vo)/Rf Since va= 0

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**The Difference Amp If R1/R2 = R3/R4 then vo = R2/R1 (v2 - v1) or**

Apply KCL at node a (v1 – va)/R1 = (va – vo)/R2 or vo = (R2/R1+ 1)va- (R2/R1)v2 Apply KCL at node b (v2 – vb)/R3 = (vb – 0)/R4 or vb = {R4/(R3+R4)}v2 Since va = vb If R1/R2 = R3/R4 then vo = R2/R1 (v2 - v1) or

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Comparator A typical comparator circuit will have one of the inputs held at a given voltage. This may often be a potential divider from a supply or reference source. The other input is taken to the point to be sensed.

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**Example: Uses a 301 op amp as a comparator.**

When vI < VT vO = - Vsat and vI > VT vO = + Vsat If VT ≠ 0V, the circuit is aptly called a threshold detector. If VT = 0 V, the circuit is referred to as a zero-crossing detector.

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**Inverting Schmitt Trigger**

Use a voltage divider to provide positive dc feedback for a 301 op amp. The circuit can be viewed as an inverting- type threshold detector whose threshold is controlled by the output. Since the output has two stable states, this threshold has two possible values, namely,

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Reference: Fundamental of Electric Circuit by Charles K. Alexander and Matthew N.O. Sadiku Lecture EE122, Stanford University, Prof. Greg Kovacs “Op Amp History.” Analog Devices. Design With Operational Amplifiers And Analog Integrated Circuits, 4th Edition by Sergio Franco https://www.globalspec.com

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