LAST month we examined the basicprinciples which allow CMOS invert-ers to be used as oscillators, conclud-ing with an example of a Colpitts oscillator.We conclude this two-part series by firstexamining a ccrystal oscillator circuit.

The high frequency crystals used to set

the clock frequency in computers canreplace L in the Colpitts circuit of Fig.10.The circuit is then sometimes called aPierce oscillator (Fig.11), although thisnomenclature is dubious.

Since a crystal blocks d.c., a resistance(R1) must be added to allow d.c. negativefeedback to set the working point. Thisresistance should be high enough not toimpair the oscillation.

Crystal manufacturers specify the valueof shunt capacitance needed to trim thefrequency to its nominal value. In the pi-net-work, the two capacitances are effectively inseries so each should be twice the quotedshunt capacitance. The frequency can be finetuned by adjusting one or both of them.

It is possible that oscillation may be tooviolent. A feedback control (VR1) mayalso be used as with the Colpitts oscillator.Crystal manufacturers may specify a safeoperating voltage and VR1 can be set to

ensure that it is not exceeded. Generallyspeaking, it is sufficient to set VR1 so thatreliable oscillation (in the face of fallingsupply voltage, etc.) is just feasible.

For crystals designed to generate fre-quencies below about 1MHz, or aboveabout 10MHz, special circuit arrangementsmay be needed. Consult the manufactur-ers data sheet.

The need for transformers or twin

capacitors can be avoided by using a so-called two-terminal oscillator circuit. Thismeans that the frequency-determining LCcircuit can be connected by just two leads,those marked X in Fig.12.

With R1 = R2, A2 has a gain close toone, so it is just a voltage inverter. Then A1must provide the gain needed for oscilla-tion. The critical condition is that VR1should be just less than the effective resis-tance of the LC circuit at its resonantfrequency fo.

The effective resistance is called thedynamic resistance and is Q times thereactance of L or C at fo. For a usable coilthe Q quality factor is unlikely to be lessthan five, and may be several hundred.

Good sine waves are obtainable at theLC circuit when VR1 is considerably lessthan the critical value, but to get a purewaveform at A2 output, VR1 must be setso that the circuit just oscillates. It may besimpler to pick off a sine wave output atA1 and extract it via buffer A3. This has again of R4/R3. The circuit may be used upto about 1MHz.

If VR1 is calibrated it can be used toobtain a reasonably accurate indication of thedynamic resistance of the LC circuit. Simplyadjust VR1 to the maximum value for oscil-lation. Then VR1 is the dynamic resistance.From this the Q can be calculated:

Q = dynamic resistance / reactance of Lor C at fo

This circuit has overall d.c. positivefeedback. It would latch up if the d.c. gainof A1 exceeded one. Fortunately, the lowd.c. resistance of L keeps gain well belowone, so it is d.c. stable.

Resistors R1 and R2 set the gain of A2to unity (1). Driving A2 directly wouldcause over-violent oscillation, The ratioR2/R1 could be increased to up the loopgain but this is not necessary with typicalLC values.

In A3, R3 and R4 set the gain and work-ing point and R3 also provides somebuffering. With VR1 set correctly there isno protection-diode conduction. Thisimplies a VR1 of slightly less than thedynamic resistance 2fLQ or Q/(2fC).However, VR1 can be less than optimumwithout seriously impairing the sine waveat the LC.

The reactive (RC) arms of a Wien bridge

(Fig.13) can be used to set the frequency ofa sine wave oscillator formed around anop.amp (Fig.14). In a Wien bridge, whenR1 = R2, C1 = C2 (the usual case) balance(zero output) is obtained when V2 = V3, inwhich case C then has a reactance equalto R.

This occurs when the input frequency finis 1/(2CR), usually called fo. Tuning isconveniently effected by using a two-gangpotentiometer for the two controlling resis-tors (R1 and R2) so that they are alwaysequal. In this way balance is maintained asthese resistors are adjusted.

742 Everyday Practical Electronics, October 2002

Part Two

Fig.11. Pierce crystal oscillator. Herethe crystal replaces L in the Colpittscircuit.

Fig.12. Two-terminal LC oscillator. A2provides the required phase inversion.A3 can be added as a output buffer.

In oscillators, use is made of the factthat RC arms of the bridge form a frequen-cy-selective voltage divider whose outputis greatest at fo. At frequencies away fromfo, output falls. When this network is usedas a positive-feedback path in an amplifier(Fig.14) and the gain is just sufficient foroscillation, a sine wave at fo is generated.

Unfortunately, the Wien network is onlyvery weakly frequency-selective. It does apoor job of discriminating against harmon-ics produced by the amplifier overloading.The waveform is distorted.

A solution used in commercial Wienoscillators for audio work is to provide a dis-tortionless means of automatically restrict-ing gain to be just sufficient for oscillation.Very pure sine waves can then be obtained.A common method is to use a negative tem-perature coefficient (n.t.c.) thermistor for theR3 resistance. As oscillation builds up thesignal warms the thermistor whose resis-tance falls. This increases the negative feed-back to the inverting input terminal, damp-ing down the oscillation.

The standard circuit (Fig.14) does nottranslate into inverter-oscillator formbecause an inverter has only one input ter-minal. It can, however, be adapted to a 2-inverter circuit, as illustrated in Fig.15.

Inverters A1 and A2 are used in theirlinear mode and the parallel-RC armnow creates negative feedback to A1 whilethe series RC arm conveys positive feed-back from A2 to A1. The circuit oscillatesat fo when the gain of A2 (adjusted byVR2) slightly exceeds two. An extra preset

scales which are very cramped at the high-frequency end. Frequency sweeps(max./min.) of 10 are then a practical limit,though the circuit will oscillate over awider sweep.

The circuit can be used as a selectiveamplifier with input injected via a high-impedance buffer A3. In this case VR2 is asharpness control and for greatest selectiv-ity is set for just not oscillating. Thebuffer amplifier may also be used, ifrequired, to inject a frequency-locking sig-nal into the oscillating circuit.

An injected signal of a few mV can syn-chronise the oscillator. How long it stayssynchronised depends on the frequencystability of both the oscillator and the syncinput. Injecting a larger signal increasesthe locking range but at the risk of falselocks where one frequency bears somefractional relation to the other. (Often thewaveform then shows some periodic dis-tortion.)

Multi-band operation is possible byswitching-in different pairs of capacitorsC. For consistent performance each pairmust be very accurately matched.

An inverter with feedback from output

to input via a capacitor (as with A1 andA3 in Fig.17) has a gain which falls offas the frequency is raised. In a sine waveoscillator this reduces the harmonicswhich result from distortion. The abilityto yield good sine waves without specialamplitude control circuitry is especiallyuseful at very low frequencies, whereconventional control using thermistors isdifficult. (The resistance of the controldevice varies over the oscillation cycleand causes distortion.)

An inverter with capacitive feedbackproduces a phase shift. Two inverters, eachgiving a phase shift of 90 in the samedirection, give a total of 180, which isphase inversion. When cascaded with asimple inverter and connected in a ring, theoverall feedback is positive at the 90 fre-quency. Here this is the frequency forwhich the reactance of C equals R.

An inverter with capacitive feedback isoften referred to as a Miller integrator, orjust an integrator. The frequency generatedby the type of circuit in Fig.17 is the sameas for a Wien network oscillator (fo =016/(RC)). With the values shown the

Everyday Practical Electronics, October 2002 743

resistance, VR1, hasbeen added. Without itthe circuit wouldcease to oscillate as Ris reduced towardszero. The oscillationfrequency is:

fo = 1/(2C(R + VR1))In fact, there is a

hidden component inthe series arm: this isthe output resistanceof inverter A2 and itmust be compensatedfor by an increasedresistance in the paral-lel arm. If this is notdone, feedback variesas R is adjusted and itis impossible toobtain a good waveform over the tuningrange.

No device for automatic amplitude lim-

iting is shown in Fig.15. The job could bedone by substituting a thermistor for thefeedback resistance across A2 as in Fig.16.VR2 would then provide oscillation leveladjustment and should have a mid-valueequal to the working thermistor resistance.

Unfortunately, there are really no suit-able thermistors available to the averagehobbyist. The sub-miniature bead thermis-tors needed are very expensive. Cheaptypes are physically too bulky and do notheat up enough at the small signal levels inthe circuit.

Vout must drive enough current throughthe thermistor to reduce its resistance suf-ficiently to obtain low distortion. SinceCMOS inverters cannot deliver much cur-rent it is desirable to keep the thermistorresistance fairly high, say 10k. The a.c.voltage across it is unlikely to exceedabout 3V r.m.s. The power available towarm the thermistor is then 09mW. Forreliable operation over a range of ambienttemperature this amount of power mustcause a temperature rise of at least 20C.

If very low distortion is not required, afairly good sine wave can be obtained fromthe circuit as shown in Fig.15 if set-upcarefully, as follows:

Set R to maximum. Set VR2 for justoscillating. Set R to minimum (zero).Without altering VR2, set VR1 for justoscillating. Repeat this procedure then, ifnecessary, make minor adjustments so asto obtain the best compromise perfor-mance over the tuning range.

The final result will depend on how wellthe two sections of the potentiometer arematched. Linear-law two-gang pots areusually better than log-law, but give tuning

Fig.13. Wien bridge.

Fig.14. Wien bridge oscillator using anoperational amplifier.

Fig.16. Using a thermistor in place ofRF in Fig.15.

Fig.15. Inverter gate version of Wien oscillator. The A3 sec-tion can be added to inject an external synchronising signal.

range is roughly 300Hz to 3300Hz. Therange can be switched by substituting otherpairs of capacitors, accurately matched.

When R is in megohms and C is inmicrofarads, the frequency is in Hertz(Hz). Because of the good discriminationagainst harmonics it is easier to achieve arespectable sine wave than with the Wienoscillator.

The circuit also has the useful propertyof yielding two equal output voltages (V1and V2) phased 90 apart (in quadra-ture). On the other hand setting up toachieve a good performance over the tun-ing band (by adjusting VR1 and VR2)involves using an oscilloscope and doing afair amount of fiddling.

Start with VR1 and VR2 set halfway.Trim VR1 to equalise V1 and V2. TrimVR2 for the best waveform. The tuningrange is somewhat affected by these set-tings. To achieve the best amplitude sta-bility one of the fixed resistances inseries with the tuning resistances mayneed to be trimmed (at the h.f. end of theband).

The three inverters of Fig.18a are con-nected in a loop or ring. If the input to A1is positive then the output of A3 is nega-tive. Since this is fed back to A1, it oppos-es the positive input. The ring is a negativefeedback loop with total feedback and(accidents barred) it will be stable.Accidents do happen, though, as will beshown later.

Referring to Fig.18b, if we now inter-pose between successive stages networkswhich produce 60 phase shift to signals at

some frequency then, going round theloop, the three phase shifts add up to 180.This is inversion.

The reactance is twice the resistance forseries C, shunt R, and the reverse for seriesR and shunt C.

The fed-back signal at A1 is now in stepwith the original signal. Feedback is there-fore positive and the circuit oscillates. Ifthe 180 phase shift occurs at only one fre-quency then that will be the frequency ofoscillation.

Two standard ways of achieving phase

shift are shown in Fig.18c to Fig.18d. Thefirst is passive the required 60 shiftoccurs at the frequency at which theseries arm has twice the impedance of theshunt arm. At that frequency the attenua-tion factor is two (i.e. half the voltage islost). This is likely to be much less than

the gain of an inverter so the circuit oscil-lates strongly.

Unfortunately, the strong oscillationdrives the internal protection diodes intoconduction. The effect is to raise the fre-quency spectacularly but unpredictably. Itwould be possible to add swamping resis-tances but a better alternative is to use thecircuit in Fig.18d. Here the phase shiftingis done by incorporating the RC networkinto an integrator, the amplifier being oneof the inverters. The inverter input terminalis now a virtual earth point and the signallevel there is low enough to avoid the worsteffects of protection-diode conduction. In aring of three such integrators each pro-duces a lagging phase shift of 60. Theoscillation frequency is theoretically

fo = 008/(CR)As before, fo is in Hertz when CR is in

megohms times microfarads and so on.

If, in circuits using Fig.18c, the resis-

tances and capacitances are reduced to zerothe circuit reverts to that in Fig.18a. Itmight be expected to display a stubbornstability. Far from it! It oscillates, but at ahigh frequency.

The explanation is simple. We mayhave removed our Rs and Cs but the cir-cuit has its own built-in equivalents. R isnow the output resistance of each invert-er and C the input capacitance of thefollowing one.

In a particular case R might be 10kand C might be 10pF. These act like thosein Fig.18c. The 60 frequency is:

fo = 1/(RC) = 3MHz approximately.

Both the output resistance and the inputcapacitance of an inverter are affected bythe operating voltage. The output resis-tance is especially strongly affected.

In experimental tests using a CMOS4069 inverter, biased to operate in the lin-ear region of the input/output curve, theoutput resistance measured 16k whenVCC was 5V, falling to 5k when VCC was15V.

This means that the zero componentring of Fig.18a is in reality a voltage-con-trolled oscillator, with VCC as its controlvoltage. Oscillation may be possible atVCC down to 2V, where the frequency isquite low. At high VCC it may be tens ofmegahertz.

Note that there is a real risk, at high VCC,of the current drawn becoming excessiveand overheating the chip. Note also thatwhile standard CMOS i.c.s like the 4069

744 Everyday Practical Electronics, October 2002

Fig. 17 Dual-integrator oscillator. Oscillation level is set by VR2. The two outputs V1and V2 are equalized by VR1 and are 90 apart in phase.

Fig.18. (a) Three-inverter ring. (b) With added phase-shift circuits. (c), (d)Alternative phase shift networks.

Fig.19. Dual-quadrature oscillator. Each twin RC network produces 90 shiftat fo.

are rated to work at up to 15V their modernequivalents like the 74HC04 have muchlower maximum VCC ratings.

It is possible to bring down the fre-quency while retaining voltage control.Add real capacitors for C while leavingR at zero.

A ring with three equal phase shifters

(Fig.18b) is a neat means of generating athree-phase signal. But suppose you needsome other number of phases. Any numberover two can be provided, with one precau-tion. The total number of inverters in thering must be odd. If it is even there is over-all d.c. positive feedback and the circuitlatches up.

If you need an even number of phasesyou have to add one plain inverter (with noassociated phase shift components) to keepthe d.c. feedback negative.

One potentially useful arrangement is tohave four shifts of 45 each. This enablesoutputs to be selected at multiples of 45,notably 90. The necessary fifth invertercan be used as a gain-adjustable stage to setthe oscillation level. The frequency is thatat which R and C have equal impedances,i.e. fo = 1/2CR.

The loop shift must be 180. For a 3-sec-tion phase shift the average per section mustbe 60, for four sections 45, and so on.

It is also possible to generate outputsphased 90 apart with a 3-inverter ring(Fig.19). Here two pairs of double RC net-works each generate a 90 shift. The fre-quency is about 1/(2RC).

In theory, three or more RC (or CR) net-works can be cascaded to give an overallphase shift of 180. A single inverting ampli-fier can then maintain oscillation, see Fig.20.

These circuits are usually referred to asphase shift oscillators (though of coursephase shifting is involved in all the oscilla-tors we have just been discussing).

Phase shift oscillators may look neatbut they have two major disadvantageswhich stem from the fact that the secondRC section loads the first, the third loadsthe second and so on. This greatlyincreases the attenuation at fo. For anetwork with three cascaded RC or CR

sections, all withequal R and C, thegain needed to sus-tain oscillation isnearly 30. For a four-section network it isnearly 20. A singleinverter may not pro-vide enough gain.

The second snag isthat it is no longerpossible to pick offoutputs evenlyspaced-out in phase.Also, the voltagediminishes at eachsuccessive section.

A third problem isthat the gain is notreadily adjustable. If,however, one inverterprovides more thanenough gain a reduc-tion can be made byshunting off some ofthe current into a sec-ond inverter (Fig.21),which presents a loadof R1 and can be used as an output buffer.(This trick can be used with other oscilla-tors.)

For a three-section RC network fo =039/RC. For a four-section RC network fo= 019/RC.

Attenuation can be reduced by taper-ing the networks. Successive resistancesare multiplied by a factor N and successivecapacitances divided by N. As N is madevery large the 3-section attenuation factorfalls towards eight and the 4-sectiontowards four. Making N = 10 achievesmost of the improvement and even N = 2 isworthwhile.

The RC network discriminates againstharmonics and even if the input to a multi-section network is a square wave the outputis a fairly pure sine wave. However, itoccurs at a high-impedance point and canonly be used if picked off by a very highimpedance buffer. This adds its own quotaof distortion.

Phase shift oscillators are fascinating

circuits which over their long history

(they go well back into the valve era)have elicited from circuit analysts someformidable feats of mathematics. But ifyou need a low-distortion oscillator youwill be well advised to leave them aloneand stick to Wien or dual-integratorcircuits!

Whilst we have concentrated on the useof basic CMOS inverter gates, the princi-ples can equally well be applied throughthe use of dual-input inverting gates, suchas NAND and NOR.

Everyday Practical Electronics, October 2002 745

Fig.20. Phase-shift oscillators. (a) Three-section RC. (b)Four-section RC.

Fig.21. Gain-adjustment circuit. R1acts as a load on A1.

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