Operational Amplifiers (Op-Amps) - Revision history

Andrew Long: /* Op-Amp Applications */

2010-01-08T22:47:41Z

Op-Amp Applications

Lynch: /* Voltage Follower */

2006-08-03T21:04:38Z

Voltage Follower

Hwang: /* Ideal Op-Amps */

2006-07-28T01:39:58Z

Ideal Op-Amps

Hwang: /* Ideal Op-Amps */

2006-07-28T01:36:06Z

Ideal Op-Amps

Hwang: /* Real Op-Amps */

2006-07-28T01:22:45Z

Real Op-Amps

Hwang: /* Real Op-Amps */

2006-07-28T01:20:04Z

Real Op-Amps

Hwang: /* Ideal Op-Amps */

2006-07-28T01:15:56Z

Ideal Op-Amps

Hwang: /* Summer With Gain */

2006-07-13T16:58:30Z

Summer With Gain

Hwang: /* Summer With Gain */

2006-07-13T16:58:04Z

Summer With Gain

Hwang: /* Summer */

2006-07-13T15:42:56Z

Summer

@@ Line 160: / Line 160: @@
 ===Controllers===
 ==References==
 Hayt, William H. Jr., Jack E. Kemmerly, and Steven M. Durbin. <u>Engineering Circuit Analysis</u>. 6th ed. New York:McGraw-Hill, 2002.

@@ Line 59: / Line 59: @@
 [[Image:opamp_voltage_follower.gif]]
+Combining the voltage follower with the
-We can put this into our [[Diodes_and_Transistors#Push-Pull_Follower|push-pull follower]] to reduce the amount of current needed to drive the circuit and eliminate crossover distortion.
+[[Diodes_and_Transistors#Push-Pull_Follower|push-pull follower]], we get the benefits of both:
+zero crossover distortion (due to the op amp) and large output currents (due to the push-pull
+transistors).
 [[Image:opamp_voltage_follower_with_pushpull.gif]]

@@ Line 11: / Line 11: @@
 .  The output voltage satisfies <math>V_{out}=A ( V^+ - V^- )</math>, where <math>V^+</math> and <math>V^-</math> are the voltages at the noninverting and inverting inputs, respectively. <math>A</math> is typically very large, such that we can consider it to be infinite.  In practice, the output voltage cannot go beyond the power supply '''rails'''.
-A consequence of this is that if there is any connection from the output to the ''inverting'' input, the op-amp will do its best to keep the voltages at the two inputs equal.  This is called '''negative feedback'''.
+A consequence of this is that if there is any connection from the output to the ''inverting'' input, the op-amp will do its best to keep the voltages at the two inputs equal.  This is called '''negative feedback'''.  ''(Note that the op-amp won't track voltages if you connect the output back to the positive input).''
 . The input current draw is zero&mdash;no current can flow in or out of the input terminals.  In practice, the input impedance is on the order of <math>10^6</math> to <math>10^{12}</math> ohms.

@@ Line 11: / Line 11: @@
 .  The output voltage satisfies <math>V_{out}=A ( V^+ - V^- )</math>, where <math>V^+</math> and <math>V^-</math> are the voltages at the noninverting and inverting inputs, respectively. <math>A</math> is typically very large, such that we can consider it to be infinite.  In practice, the output voltage cannot go beyond the power supply '''rails'''.
-A consequence of this is that if there is any connection from the output to the inverting input, the op-amp will do its best to keep the voltages at the two inputs equal.  This is called '''negative feedback'''.
+A consequence of this is that if there is any connection from the output to the ''inverting'' input, the op-amp will do its best to keep the voltages at the two inputs equal.  This is called '''negative feedback'''.
 . The input current draw is zero&mdash;no current can flow in or out of the input terminals.  In practice, the input impedance is on the order of <math>10^6</math> to <math>10^{12}</math> ohms.

@@ Line 24: / Line 24: @@
 <u>'''Input Bias Current'''</u>: This is the average current that flows through the two inputs.
-<u>'''Saturation'''</u>: The output voltage is bounded by the positive and negative power supplies, known as '''rails'''.  In fact, many op-amps will only go up to a few volts short of rails.  If we look at the '''Output Voltage Swing''' in the data sheet for the LM411, we see that under a &plusmn;15V power source, the output will will generally be able to swing between &plusmn;13.5V&mdash;but you just might get a chip that can only output &plusmn;12V.  Op-amps that are designed to be able to output voltages very close thier rails are refered to as being '''rail to rail'''.  '''The absolute values of your rails should be the same.'''
+<u>'''Saturation'''</u>: The output voltage is bounded by the positive and negative power supplies, known as '''rails'''.  In fact, many op-amps will only go up to a few volts short of rails.  If we look at the '''Output Voltage Swing''' in the data sheet for the LM411, we see that under a &plusmn;15V power source, the output will will generally be able to swing between &plusmn;13.5V&mdash;but you just might get a chip that can only output &plusmn;12V.  Op-amps that are designed to be able to output voltages very close thier rails are refered to as being '''rail to rail'''.
 <u>'''Slew Rate'''</u>: The output voltage cannot change instantaneously; the maxiumum rate of change possible for the output voltage is known as the '''slew rate'''.

@@ Line 9: / Line 9: @@
 Op-amps are generally very well described by their ideal model.  There are several basic rules for ideal op-amps:
-.  The output voltage satisfies <math>V_{out}=A ( V^+ - V^- )</math>, where <math>V^+</math> and <math>V^-</math> are the voltages at the noninverting and inverting inputs, respectively. <math>A</math> is typically very large, such that we can consider it to be infinite.  In practice, the output voltage cannot go beyond the power supply ''rails''.
+.  The output voltage satisfies <math>V_{out}=A ( V^+ - V^- )</math>, where <math>V^+</math> and <math>V^-</math> are the voltages at the noninverting and inverting inputs, respectively. <math>A</math> is typically very large, such that we can consider it to be infinite.  In practice, the output voltage cannot go beyond the power supply '''rails'''.
-A consequence of this is that if there is any connection from the output to the inverting input, the op-amp will do its best to keep the voltages at the two inputs equal.  This is called ''negative feedback''.
+A consequence of this is that if there is any connection from the output to the inverting input, the op-amp will do its best to keep the voltages at the two inputs equal.  This is called '''negative feedback'''.
 . The input current draw is zero&mdash;no current can flow in or out of the input terminals.  In practice, the input impedance is on the order of <math>10^6</math> to <math>10^{12}</math> ohms.

@@ Line 108: / Line 108: @@
 <math>i_1=V_1/R_1</math>&nbsp;&nbsp;&nbsp; <math>i_2=V_2/R_2</math>&nbsp;&nbsp;&nbsp; <math>i_3=V_3/R_3</math>
-<math>V_{out}=-R_F\left\frac{V_1}{R_1}+\frac{V_2}{R_2}+\frac{V_3}{R_3}\right</math>
+<math>V_{out}=-R_F\left(\frac{V_1}{R_1}+\frac{V_2}{R_2}+\frac{V_3}{R_3}\right)</math>
 ====Summer Without Gain====

@@ Line 97: / Line 97: @@
 ===Summer===
+====Summer With Gain====
 [[Image:opamp_summer_gain.gif]]
@@ Line 109: / Line 110: @@
 <math>V_{out}=-R_F(\frac{V_1}{R_1}+\frac{V_2}{R_2}+\frac{V_3}{R_3})\,</math>
+====Summer Without Gain====
+If we do not want the summer to apply any gain to the inputs, simply choose all the resistor values to be the same.
 [[Image:opamp_summer.gif]]