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Most recent update 10-26-2011

About RC audio range low-distortion oscillators

General performance issues
Low distortion is desirable for testing high performance audio equipment and constructing AC voltage reference standards, for excitation oscillators in high-resolution AC bridges, and for other high-resolution measurements at audio or sub-RF frequencies. There is an obvious trade-off between wide frequency range, low distortion, and stability. Single frequency or narrow-range spot frequency oscillators can usually be simpler and better, as in the Linear Technology design for a 10kHz oscillator, which while not exactly simple, offers THD in the low parts per billion area.

RC oscillators work by having both negative and positive feedback, with the gain from positive feedback slightly higher than the loss from negative feedback. One feedback path goes from the output of the system amplifier through a frequency-selective band-pass or band-reject filter, which enables the amplifier to oscillate only at a single frequency. Then some form of automatic level control (called ALC or AGC) is needed to stabilize the operating point of the system. This stable operating point provides output amplitude stability and low distortion, if the amplifier is a good one.

In general, the audio range oscillator's amplifier must be low noise, have good to excellent CMRR, and be relatively wide-band, with a GBW product of 5MHz or more, preferably more, if operation at high frequencies, such as 100-200kHz, is desired. IC op-amps are naturals for this use, with several having wide commercial application, including the Signetics/TI NE5534 and the Harris/Intersil 2600 series. Other candidates include the Analog Devices AD797, the Burr-Brown/TI OPA134. OPA604, and OPA1641, and several Linear Technology parts, such as the LT1115, LT1122, and LT1468. Low noise, high gain and low distortion are the key parameters. Low-noise FET-input op-amps, like the OPA134 and 1641 can offer lower noise when the filter impedance is relatively high, as is often the case in Wien Bridge and Bridged-T designs -- especially those in which variable capacitors do the tuning. A FET input amplifier is essential for the very widely-used capacitively-tuned Wien Bridge units due to the necessarily small capacitors and very large resistors needed for range setting at low frequencies.

Any of these designs can work very well, given good amplifiers, careful layout, precision components, and tight AGC. No one design has proven conclusively better, although the state-variable design is in ascendency in RC oscillators. Good RC oscillators still find favor with audio system designers, audiophiles, and hobbyists thanks to simplicity and low cost.

Although they are being rapidly replaced in commercial and industrial applications by Direct Digital Synthesis (DDS) designs, RC oscillators for low-frequency, low-distortion use are still popular and generally take one of a few forms that offer relative simplicity and economy of design with good overall performance. Modern amplifiers and good design can yield 1kHz THDs of well under 1ppm, or 0.0001%, although very special analyzers are needed to detect the distortion with accuracy. Here are the basic designs:

Wien Bridge
This circuit is famously the heart of the HP 200 Series, and is used in many others, including the Heath IG-1272 and some Sound Technology units. It uses a series arm of an R and a C connected to a parallel arm having the same R and C component values. This filter is then placed in the positive feedback loop of an amplifier, with the junction of the series and parallel arms connected to the non-inverting input. Meanwhile, an automatic gain control circuit is placed in the negative feedback loop and connected to the inverting input.

Wien bridge

If the Rs and Cs are equal in the two arms, the amplitude of the tuned feedback signal through the bridge to the non-inverting input is 1/3 the amplitude (-9.5dB) of the output and, compared to the output, has a phase shift of 0 degrees at f = 1/(2* Pi*R*C), which is the frequency of oscillation. The 0 degree phase shift at the bridge's peak amplitude, coupled with the 0 degree phase of the amplifier, results in 0 degrees of phase shift only at the oscillation frequency -- any other frequency has more or less phase shift, and higher attenuation, preventing oscillation.

The negative feedback network to the inverting input of the amplifier needs to have an attenuation of slightly more (a gain of slightly less) than 3, so that positive feedback slightly exceeds negative feedback to sustain oscillation. The negative feedback also has the effect of sharpening the Wien Bridge filter, increasing its Q and increasing the slope of the phase shift through zero.

Wien plot

Wien-Bridge peak filter response before feedback is applied

Most Wien Bridge oscillators use equal Rs and equal Cs, but a few, like the HP 651/652/653/654 Series use a series arm of R 2C and a parallel arm of 2R C, which results in an attenuation of 2 instead of 3 for the peak positive feedback signal. This lowering of needed amplifier gain may have the result of lower noise or better high-frequency stability; HP doesn't say why they used this configuration in these very wide-band units instead of the classic form.

Wien Bridges can be effectively tuned within a range either by variable capacitors or by variable resistors, or they can be tuned in discrete steps with either switched Rs or Cs as the variable elements. Ranging is then done with the other components, either Rs or Cs. Most low-cost RC audio oscillators are capacitance tuned -- it seems to be easier and cheaper to make precision dual-gang tuning capacitors than to make precision dual-gang log taper potentiometers.

John L. Linsley Hood argued that the primary weakness of Wien Bridge oscillators was that they are limited to around 0.01% THD due to relatively high input signal levels to the amplifier and a resulting common-mode failure in the input stage(s). Jim Williams of Linear Technology designed a Wien Bridge oscillator using IC op-amps, with an op-amp driving both the common point of the bridge and AGC common to create a virtual ground and suppress the common-mode signal, and he reported a significant reduction in THD, to a level of about 3ppm (see Linear Tech. App Note 43, p. 31 -- but note that the text description for Fig. 48 and its common-mode suppression technique actually applies to Fig. 47, and vv.).

These circuits, famously used in the Heathkit IG-18/SG-18 and successors, and the HP 239A Oscillator (and the oscillator section of the HP 339A Distortion Analyzer), place the filter circuit in the negative feedback loop of the amplifier and the AGC circuit in the positive loop. Again, the frequency of oscillation is given by 1/(2*Pi*R*C), but with a twist. The filter uses a bridge capacitor, Cb, to bridge the two resistor arms, with a second pillar capacitor, Cp, from the junction of the two (equal) resistors to common. The result is a notch filter whose depth depends on the ratio of the two capacitor values.

The square root of the capacitor ratio is a multiplier and divisor of the C in the frequency formula in order for the tuning frequency to be as calculated. Placed in the negative feedback loop, the notch becomes a peak at the amplifier's output. At frequencies on either side of the notch/peak, the overall negative feedback keeps oscillation from occurring. The AGC is in the positive feedback loop, and the attenuation in that loop has to be slightly less (the gain from the loop slightly more) than the attenuation at the notch frequency in the negative loop to sustain oscillation.


The notch attenuation of the Bridged-T is given by 2/(2+[Cp/Cb]), that is, 2/(2+Cratio). The value of the two capacitors is given by the C in the f = 1/(2*Pi*R*C) formula, with
Cbridge = C/[sqrt(Cratio)]
Cpillar = C*[sqrt(Cratio)]

In the Heath IG-18, the ratio of the capacitors is 10:1, meaning that Cb = C/3.162, and Cp = C*3.162. This ratio gives an attenuation of 2/(2+10) = 1/6, or about 15.6dB if the capacitor values are precise. This in turn means that the gain from the positive loop has to be slightly more for oscillation.

Heath Bridged-T

Bridged-T notch filter response before feedback is applied

In the HP 239A/339A, the capacitor ratio is 100:1, with an attenuation of 2/(2+100) = 1/51, or slightly more than 34dB, and Cb = C/10, Cp = C*10. Positive loop gain has to be a bit over 34dB. The higher gain and bigger ratio of the HP design means a sharper and deeper notch with higher Q, which gives better frequency selectivity, leading to lower THD if the amplifier is quiet and has intrinsically low distortion. Thanks to the very high filter gain and a very good opamp, the HP 239A (and the HP 339A) achieves extremely low THD at 1kHz, under -110dB and approaching 1ppm.

July 2011 Update -- I recently looked at the schematics for the Krohn-Hite 4400A and 4402B. These units in fact use a Bridged-T oscillator with equal capacitors for bridge arms, and unequal resistors for the bridge and pillar components. They have a bridge-to-pillar resistor ratio of 2, which leads to a fairly low-Q, 6dB peak in the system response at the tuned frequency. I suspect but can't prove that the low-Q oscillator helps to give the units their excellent settling-time specs. The 4402B has specs comparable to the HP 239A, but I have no way of knowing whether they are comparable in actual use. The K-H units are very highly regarded instruments.

The Heath IG-18 design uses 5 capacitors to do the work of 8 (for 4 ranges) because the range switching swaps the 10:1 ratio caps from bridge to pillar position as the ranges step up in decades. The Heath design has about the minimum ratio that will work well, given that Q goes down as the ratio decreases.

The HP 239A design uses 8 capacitors, and has about the largest practical capacitor ratio both from an amplifier gain point of view and because of the total span of capacitance needed for wide range, from microfarads to picofarads. If fewer ranges are used, then a larger ratio is possible -- if the amplifier's noise and intrinsic THD performance will support it.

Compared to the Wien bridge, the notch filter of the Bridged-T, especially one with a large Cp/Cb ratio, has a fairly steep phase slope, and has higher Q. But a countervailing factor is the extra amplifier gain needed, especially if the Q is very high; as noted, this means the amplifier has to be very quiet and have very low intrinsic distortion, as well as having very high open-loop gain.

1-9-2011 -- In looking at this page again, I noticed that I had forgotten to mention that there is another arrangement for the Bridged-T, one in which the arm elements of the T are equal capacitors, and the unequal bridge and pillar elements are resistors. In this arrangement, the bridge resistor is the larger and the pillar resistor is the smaller, opposite to the case for the bridge and pillar capacitors described above -- same calculations, just the location is reversed.

This arrangement is useful for capacitance-tuned oscillators, but does result in large resistor values at low frequencies for the typical relatively small capacitances of ganged air-variable tuning caps. I remember that Heath used this arrangement in one of their vacuum tube sine wave oscillators, but I don't remember which model that was.

1-14-2011 -- I have recently gotten an HP 339A in for check out. I had to repair and calibrate it before I could evaluate the oscillator, but the bottom line is that the oscillator in the 339 is better than it's analyzer circuitry, which itself is pretty good. Using my Active Twin-T filter and the software spectrum analyzer, with a 1kHz fundamental the only significant distortion product is the 2nd harmonic, and it is at -120dB. The rest of the THD and IMD products are below -120dB. I estimate the THD at less than 0.0003%, with THD+noise well under 0.001%, if 400Hz high-pass filtering is used. Very nice performance. I can't tell what the oscillator IC is; I speculate that it is from the Harris/Intersil 2500 or 2600 series The opamp is an HA-2625, a high-gain, wideband opamp that was also used in Sound Technology units .

The AGC loop in the oscillator uses half-wave rectification, which is surprising to me, given its very low distortion, followed by a buffer that drives an integrator, which then drives a JFET as the active control element. Drain-to-gate feedback around the JFET is a standard 50% for 2nd harmonic cancellation. It works. I find it interesting that HP didn't use an LED-photocell combination for AGC, since they do use it in the 339 for auto set-level.

The 339's oscillator design has me rethinking bridge-type oscillator performance -- I've sold it a little short. If Jim Williams' active common-mode cancellation around a Wien bridge circuit works as well as this Bridged-T, then high-performance oscillators can be a bit simpler than I had thought.

These circuits, including the high-performance Tektronix SG-505, and the oscillator section of Bob Cordell's THD Analyzer, as well as the Krohn-Hite 4400A (I think -- I haven't seen a circuit diagram), employ two inverting amplifier integrator stages, each with an R C tuning section of an R input element and a C feedback (integrator) element, with one element, usually the resistor, tuning the frequency within a range, and the other element tuning the range. The sections have identical gains and time-constants, meaning equal Rs and equal Cs. Alternately, the similar phase-shift oscillators can have more than two tuned stages, but then tuning obviously is more complicated.

In a two-integrator design, each integrator has 90 degrees of phase shift at the tuned frequency, for 180 degrees. Feedback is applied overall via a third inverting amplifier, with an additional 180 degrees of shift to get the required 360 degrees of phase shift of the output back to the input at the oscillation frequency (all oscillators, like the Wien Bridge, can properly be described as phase-shift designs, but most are separated out from this class thanks to using peak or notch filters, rather than the sequential low-pass filters of this design). The frequency of oscillation is once again 1/(2*Pi*R*C).

Like the Wien bridge, the gain control feedback, usually to the third amplifier, must be such as to maintain oscillation. The amplifiers of these oscillators are generally set up for unity-gain. An advantage of the state-variable design is that it can be set up, as in Cordell's design, to allow independent fine-tuning of frequency for each range by changing one feedback resistor value per range. These oscillators are capable of very low distortion levels of anywhere from 2 to 20 ppm at audio frequencies, depending on amplifier quality and noise levels, and on the performance of the AGC loop.

As noted by Bob Cordell, an intrinsic advantage is that the output can be taken from the second integrator stage, yielding a built-in 2nd-order low-pass tracking filter having -12dB/octave response above the frequency of oscillation, which greatly reduces both distortion and noise in the output. But by far the greatest advantage is that these oscillators use an all-inverting amplifier topology, which intrinsically prevents op-amp common-mode errors from occurring.

These circuits are almost never used in commercial designs because they require 3 capacitors and 3 resistors for tuning, meaning 6 parts per range rather than 4 for the other designs, with a consequent increase in tuning complexity -- not economical, not practical, and no particular performance benefit. Twin-T designs are generally better suited to manual tuning, but since the performance doesn't justify the complexity, they are rarely used.

Oddly, though, HP used a Twin-T notch filter in a THD analyzer, the 4333A, a unit I've never seen, and which may not have had much market life -- quite a complicated tuning system was used in its design. This unit was a nearly all-discrete transistor unit that followed the 334 and preceded the 339. I suspect it had moderately high performance, but the circuit complexity may have been problematic.

Automatic Gain Control
Incandescent lamp based -- AGC is essential in a low-distortion oscillator and is often controlled by using an incandescent lamp as either a ground leg resistor or a feedback resistor in a feedback loop. A lamp is a positive temperature coefficient (PTC) resistor. As the output increases, the level of the feedback current increases, the lamp gets hotter, its resistance increases, and the amplifier gain goes up or down, as needed by the particular configuration. Very elegant and quite effective, and also economical. THD performance can be as good as 0.01% or a bit better at fairly high output levels -- the Heath IG-18 has output of 10VRMS into a high-Z load or open-circuit from less than 10Hz to over 100kHz. The HP 200CD has 20V open-circuit from 5Hz to 600kHz. Both use high-voltage, low-wattage lamp types -- one 90V lamp in the Heath and two 120V lamps in the HP.

10-26-2011 -- See my page Lamps for oscillators for a discussion of lamp characteristics for use in oscillators. Lamps work well in filter circuits with relatively low gain, as in the IG-18, but do not have enough dynamic range, that is, do not have enough resistance change with level change, to work well in high-gain variable frequency oscillator applications where the change in frequency -- and the resulting change in filter gain -- is large. However, I recently have breadboarded an oscillator based on a very high-gain bi-quad band-pass filter, that uses a couple of 2187 lamps for stabilization and achieves better than 0.0005% THD; just don't change the frequency very much.... But that gave me a whole new perspective on the ability of lamps to deliver high performance.

Thermistor based -- Another common and simple AGC system is to use a thermistor, a negative temperature coefficient (NTC) resistor, as one leg of the feedback loop. Thermistor-stabilized oscillators include the well-known GR 1310-A. With the thermistor, as the signal current increases, its resistance decreases, raising or lowering the gain as needed by the configuration. Both lamps and thermistors are effective, but being first-order systems, directly controlled by the output signal level, they are limited in the tightness of the level control they can achieve. Thermistors have the added disadvantage of being sensitive to ambient temperature conditions, complicating stability unless the heating due to signal current is high enough to swamp ambient effects.

Thermistors have the added liability of having to be physically extremely small and fragile in order for the signal current to heat them enough to result in a significant resistance change. And when small, they are even more sensitive to ambient effects. GR got around this problem by encapsulating tiny thermistors in vacuum bulbs, much like lamps. This has two advantages -- one, they are effectively isolated from ambient temperature, and two, they have a longer thermal time constant thanks to the absence of significant heat conduction into air. Such thermistors are now unobtainable -- at least I haven't been able to find any; this may mean a change from a thermistor system to a lamp system if the thermistor in an older oscillator is damaged or destroyed. Fortunately this is not difficult, but it can be a major change.

In general, performance is about the same as a lamp type AGC unless special techniques are used. John L. Linsley Hood designed one oscillator using a thermistor and a Wien Bridge, tuned with a two-gang potentiometer, that achieved THD less than 0.005% in the 100Hz to 10kHz range (Low distortion oscillator, Wireless World, September 1977). He also designed a unit that employed a multiplier type of feedback with a thermistor that balanced positive and negative feedback from a split-load phase inverter (Spot-frequency distortion meter, Wireless World, July, 1979). This design achieved very low THDs of less than 0.0003% in the 100Hz to 10kHz range. This elegant design did use a Twin-T filter circuit with elements switched for spot frequency use, continuous tuning being impractical. Unfortunately, as noted above, the thermistors he used have long since disappeared from the market, and it's not possible to replicate his designs.

JFET based -- Today, many AGC systems use the channel resistance of JFETs as gain control elements, sometimes as part of a multiplier system in the feedback loop of an op-amp, as in Bob Cordell's design, where a balance of positive and negative feedback is maintained such that very small changes in output signal amplitude result in a shift in the balance of the two types of feedback in the gain control stage. The control is by a DC signal derived from the AC output by rectification and filtering, and one or more stages of integration and/or amplification to achieve high loop gain and very tight control. As an N-channel JFET's gate-source voltage becomes less negative and approaches zero, the drain-source resistance decreases. When the FET is placed in the common leg of a feedback network, this means an increase in output will drive the gate-source voltage more negative, raising the channel resistance and reducing the overall gain, lowering the output, and vv.

JFETs work very well when the signal level controlled by the channel resistance is low, generally less than a few hundred millivolts, with lower being better; and when local feedback from drain to gate or from output signal to gate is used to reduce channel resistance modulation effects -- see Jim Williams' notes on this effect. Bob Cordell says the key to low THD is to keep the signal level on the FET's drain low, well under 100 millivolts, which is not usually the case in units like the HP 204C/D, which only manage optimized THDs of around 0.05% -- otherwise they are very capable FET-stabilized wide-range oscillators.

In general, THD performance of well-designed JFET-controlled oscillators can be in the 0.2ppm to 200ppm range (0.00002% to 0.02%), depending on operating range and other details, as noted previously.

Photocell based -- Other AGC systems use a Cadmium-Sulphide (CdS) photocell as a purely resistive feedback control element, with its resistance controlled by a lamp or LED powered by a DC signal derived from the AC output signal. The DC signal is conditioned by one or more amplifiers and/or integrators. Unlike a JFET, the photocell is purely resistive, and is free from internal modulation effects (although the DC has to be fairly well filtered and have low signal ripple to avoid modulating the photocell, especially when driven by an LED -- see the designs by Jim Williams in Linear Technology App Note 43 for examples of applying photocells.

These days, photocell-lamp assemblies are hard to find, but are still easily constructed from a relatively small (8mm dia.) CdS cell and a green LED (CdS cells are most sensitive in the green part of the spectrum). They can be placed in some black heat-shrink tubing or other rigid or semi-rigid light-blocking material to hold them together. Photocells do not have a fast response to changes in light intensity, an effect analogous to the thermal mass of an incandescent lamp or a thermistor. Using an LED light source instead of an incandescent lamp naturally improves the response. But the CdS systems are still fast enough that extra loop filtering is needed for stability.

THD performance can be equal to or perhaps slightly better than JFET based designs, but the photocell based AGC systems are rarely used in commercial designs, where the JFET systems dominate. I suspect that JFET designs are preferred for both cost and board-space reasons. Some commercial products, notably from Sound Technology, have used both JFET and photocell loops in the same oscillator to gain both rapid response and low distortion.

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