Oscillations and Voltage-Controlled OscillatorsTiming-based Oscillators (see Grebene)Practical Implementations (i.e. the 566)Details about the Timing and Schmitt TriggerImplementation of Current Sources (and “diode steering” of currents)Something really scary…Now for a “more challenging” OscillatorDetailed Equations…See T. Lee Book…A Colpitts Oscillator ExampleThe Simplified Explanation1Oscillations and Voltage-Controlled Oscillators• Feedback perspective A=a/(1-af), if af=1 we get infinite gain…or oscillations• From EE 122 the phase-shift oscillator specifically uses series-parallel RC network to:– Make |f|=1/|a| and– Guarantee exact 0-degree phase shift• Timing-based oscillations--this can be “ring oscillator” type or “charge-discharge” (of C) type• Transistor level oscillations (which we’ll do now)This discussion, while couched in terms of oscillators, has relevance to amplifiers as well--often in terms of considering how to make the amplifier NOT oscillate.Also, please refresh your memory about the general feedback expression (aka EE113/101B) since it is critical when considering impedances as well as gain expressions.There is LOTS to say about kinds of oscillators--phase-shift versus relaxation-, ring-type etc.Also, it is important to differentiate between sinusoidal oscillations (a single “tone”) versus (ring- and) relaxation-type oscillators that create triangle or square-wave oscillations.In lab you will have a chance to consider both a sinusoidal oscillator (the so-called “Colpitts” oscillator, named after its inventor) and a relaxation-type oscillator.Oscillators (and VCO)2s (=jω)σ−σ +σReminder abouts-plane and polesmoving into eitherLHP or RHPR1R2(-)(+)InvertingGain amp.Av~ -R2/R1Phase-shiftNetworkφ=0 and foand attenuatingby 1/AvQuick reminders from EE122 (and EE102/101B about the s-plane plot) concerning the “phase shift” oscillator.This oscillator has two key kinds of feedback:1) The classical R1-R2 “negative” feedback, which gives a voltage gain as indicated and2) Feedback around the positive loop where the two [square boxes] indicate an R-C (or L-R-C)network that is frequency selective and has a unique frequency where the phase-shift is exactly zero.At this frequency (by design) the attenuation of the R-C is balanced by the gain of the R1-R2 block such that oscillations are sustained.In the s-plane we want the poles to be located exactly on the jωaxis--if they are in the Left Half Plane (LHP) the oscillations will decay away and if in the Right Half Plane (RHP) the oscillations will grow without bound…3Timing-based Oscillators (see Grebene)+VccControl Logic:S1 on (S2 off)ThenS2 on (S1 off)S1S2CTimer Circuits:•Schmitt Trigger•555 IC•Many others...I = CdVdtC∆VxI=xT“x” is the portion of thetotal period for which therespective “Ix” is in controlNow let’s turn our attention to the “relaxation-type” oscillator, shown schematically here as simply a storage element that is being charged and discharged by two current sources.Basically, there are many chips that employ this kind of oscillator; possibly the one most familiar to you would be the 555 “timer chip” where all you have to do is select the capacitor (and one resistor) to create such oscillations.The capacitor’s governing equation (differential form) is shown.For a constant-valued capacitor we can use ∆V and ∆T and for each portion of the charging (or discharging) of the capacitor ∆T becomes TXHence, the fraction of the period called out as TXis directly proportional to C and ∆V and inversely proportional to IXWe can make the wave forms symmetric or asymmetric by changing the values for IXon each portion of the waveform.Finally, although not written on this slide, the frequency of oscillation is given by the INVERSE of the sum of T1+T24Practical Implementations (i.e. the 566)The following slides come from a suplemental handout taken from Alan Grebene’s book Bipolar and MOS Analog Integrated Circuits.Alan was the lead designer who created the 555 and related products.This figure shows schematically the two current sources that charge and discharge the capacitor C1. The Schmitt trigger circuit (an old friend from EE122?) sets the voltage excursions over which the voltage VO1will travel (I.e. ∆V=VB-VA)During the charge-up period (T1) the lower current source is assumed to be “off” so that the slope of V(t) is determined only by I1.Once the voltage reaches VBthe current source I2turns on (and its value is greater than I1) so that the discharge period (T2) is determined by I2-I1.A few more details, including the equations to go with the abovediscussion, are shown on the next figure.5Details about the Timing and Schmitt TriggerT1=VB−VA()C1I1T2=VB−VA()C1I2− I1f =1T=1T1+ T2=I1VB−VA()C11−I1I2      Simple reminder about the Schmitt trigger…It provides a digital (logic H and logic L) output with a hysteresis in the transitions going L->H and H->L determined by VAand VB.In this figure VHcorresponds to VB-VAThe two fractions of the total period, T1and T2, are determined by the capacitor and current source values (as shown in the schematic on the previous page)The resulting frequency of oscillation is given by the inverse of the sum of the two times as shown.The above discussion has been rather general in terms of allowing the two currents to have arbitrary values.The next slide gets down to one specific application where in fact the current is “diode steered” such that I1=(I2-I1)6Implementation of Current Sources (and “diode steering” of currents)This schematic shows an abstracted view of what you will be using in the 566 chip.Basically, when S1is OPEN the current I1can only flow through D2and charge-up C1When S1is CLOSED, the current mirror (a so-called Wilson Mirror after it’s inventor, George Wilson and former Motorola and Tektronix designer) pulls the current I1through D1and the in turn Q2forces that same current to flow which then discharges C1In the process you can easily convince yourself that D2must be off--basically, once S1‘offers” a lower potential path for I1to flow through, the current goes that way and the potential at the “cathode” side of the diodes drops to that value [to be discussed a bit more in class…both using this figure and probably the real schematic for the 566 :)]From your perspective as USER of the 566, the control voltage (VC) sets the current