Phys 15b: Lab 6, Spring 20071REV 01; March 13, 2007.Physics 15b, Lab 6: The Op-amp: applying it to build a radioDue Friday, May 4, 2007 (this is a two-week lab), with a complication, as follows:• for the first week (April 16...), this is an ordinary “at-home” exercise, for which we run help labs as usual:– Wednesday 6-9 p.m., April 18– Thursday 3-9 p.m., April 19• for the second half of your work, we ask that you come in to lab section, in Science Center 305 as you did forLabs 1 and 2 (same section assignments; the list is posted on the course website). These lab sections run inthe week beginning April 23 or April 30: Thurs., April 26, 3 to 5:30 or 6 to 8:30; or Thurs., May 3, 3 to 5:30or 6 to 8:30.We want you to come in, for several reasons:– you need access to a good antenna, and we have one in the lab;– we want to confirm your success;– if you need to troubleshoot your circuit, it is very helpful to have the use of an oscilloscope—and thehelp of someone experienced in the use of that rather-complex instrument.Attachment: LF156/356 Data Sheet (operational amplifier)1Revisions: correct R-value of “ground” divider, from 360 to 8.2k ohm (11/06); add table of contents (3/-06); radio merged into existingLab 6, mutual inductance exercise cut (10/04); typo corrected, p. 6: multiplier is 10−9rather than 109; add suggestion to plug in N/lengthin place of n ∗ N, equation 10 (4/13/04).Phys 15b: Lab 6, Spring 20072Contents1 Purpose 22 Background 3Voltageamp.................................................... 3Currentamp.................................................... 32.1 Characterizing a Voltage Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3DCGain,ACGain................................................. 32.2 Operational Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Procedure 73.1 Creating a ±4V supply............................................... 7Preliminary Rail Splitter: resistive divider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Improved Rail Splitter: resistive divider helped by an op amp . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 WiretheOp-AmpCircuit............................................. 8SolderorBreadboard?............................................... 8Pinout of the op amp integrated circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8IfYouChooseSoldering: ............................................. 9WhicheverWayYouBuildIt:........................................... 93.3 Don’tPlugintheOp-ampYet........................................... 93.4 CheckOut..................................................... 93.5 PluginOp-amp .................................................. 103.6 Determine Gain (Gclosed−loop).......................................... 104 AM Radio Receiver (fun!) 115 Select one Broadcast “Carrier” Frequency 125.1 A “Resonant Circuit”” RLC ........................................... 13Impedances of C and L .............................................. 135.2 Calculate the LC values you want . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Wind Yourself an Inductor 156.1 Deriving or justifying the expression for Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.2 HowManyLoopsdoweNeed?.......................................... 16Some Corrections for the L Formula ....................................... 16Windtheinductor................................................. 16...add the C .................................................... 167 Build the detector 177.1 DesigntheDetector................................................ 18A Design, and Choosing R and C Values..................................... 188 Amplify the audio, and Listen 198.1 UnityGain“Amplifier” .............................................. 208.2 Listen!....................................................... 201 Purpose1. To introduce you to the operational amplifier (op-amp), used as a voltage amplifier, and then as a currentamplifier.2. To apply an op amp, along with passive components (inductor, diode, capacitors, resistors) to make an AMradio.We hope you will find it gratifyingto see that circuitsyou met earlier as fragments—diode rectifiers, filtercapacitors—when combined with a new one, the resonant LC circuit, can make something useful and pretty flashy: a radioreceiver. The amplifier will make the receiver’s output audible.Phys 15b: Lab 6, Spring 200732 BackgroundVoltage Amplifiers, Current AmplifiersVoltage ampA voltage amplifier is designed so that the voltage out of the device, Vout, is equal to the product of the voltage in,Vin, times some gain factor. This allowsyou to convert a weak, barely measurable signal to a strong, easily measuredsignal.Current ampA current amplifier presents an idea that is probably less congenial to you: we are accustomed to signals that arevoltages rather than currents2. Sometimes, however, we need to boost only current, not voltage. That turns out to bethe case in the second stage of the this lab, where we want to use headphones to listen to a signal that is not so muchsmall as feeble—incapable of driving the headphones without our help.2.1 Characterizing a Voltage AmplifierDC Gain, AC GainDC Gain Roughly, you can determine the DC gain of an amplifier by applying a voltage, Vin, to the input of theamplifier and then measuring the Voutthat results. In the ideal case, the DC voltage gain, GDC, of the amplifier issimply Vout/ Vin. Unfortunately, real amplifiers often don’t know zero in when they see it: they are said to includea “voltage offset,” so that when presented with an input of zero volts they think they see Vof fset. They then proceedto amplify that delusion. If you applied zero volts to such an amplifier, the output would go not to zero but to Vout=GDC• Vof fset. Thus, measuring DC gain accurately requires measuring Voutfor a series of Vin, or at least for bothpositive and negative Vin.AC Gain AC gain–GAC–is easier to measure, since Vof fsetis not involved. GACis just∆VOU T∆VIN. In laboratories,an AC test signal is usually produced by a “signal generator,” a device that typically produces square waves, trianglewaves, and sine waves with tunable amplitude and frequency. We hope that many of you will come to help lab anduse