The recent Design Idea “Getting an audio signal with a THD < 0.0002% made easy,” discloses a low THD sine generator which led me to dust off a design that I had published in AudioXpress magazine [1] (see Figure 1).
Figure 1 The “Simple Sineman” circuit [1] is based on a simpler version of the circuit having approximately -80dB THD [2].
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Requirements for an analog oscillator
Before getting into the detail of how this circuit works, it’s worth recalling certain requirements for an analog oscillator: a feedback circuit which, at the oscillation frequency fosc Hz, has a loop gain magnitude of unity and a phase shift of either 0 or a multiple of 360 degrees. One means of implementing this is to place a notch filter in the feedback loop of an op amp. You might be forgiven for thinking that fosc is at the filter’s notch frequency fnotch Hz. But obviously, infinite attenuation is not consistent with a unity gain loop. Not so obviously, the op amp’s internal compensation network adds a -90° phase shift to its inherent -180° inverting input-to-output phase shift. What is then needed for oscillation is a filter which, at fosc, exhibits both a -90° phase shift and has an attenuation of Aosc, where Aosc is the op amp gain magnitude at fosc. But how can we find a filter capable of meeting such precise constraints?
The “dual-T” notch filter
The innovative “dual-T” notch filter in Figure 1 saves the day. It’s made up of C1, C2, C3, R1, R2, R3A, and R3B. I had a need for a 2400-Hz oscillator and so chose the values shown. One way to place a notch at fnotch Hz is to use the following process and equations:
Choose a value C for C1, C2 and C3 (1)
and set R1 and R2 equal to 1 / (2π* fnotch*C*√3) (2)
set R3 = R3A + R3B equal to 12 / (2π* fnotch*C*√3) (3)
An analysis of this filter type shows that there is always a value of R3 which produces an infinite attenuation notch regardless of the variations of the other component values due to tolerances. Since there is clearly no attenuation at DC, this means that any attenuation from none to infinity can be had at some frequency. The analysis also shows that there is always some frequency below fnotch at which the phase shift is -90°. The appropriate value of R3 causes that phase shift to coincide with the necessary attenuation of Aosc at fosc. Figure 2 gives a feeling for some phase and gain magnitude responses of the filter as R3B is varied. Table 1 relates the oscillation and notch frequencies and values of R3 for a -90° phase shift at various attenuations Aosc.
Figure 2 Responses of the dual-T notch filter. To simulate practical variances from the ideal, capacitor values were randomly selected to be within 1% of 10 nF, and R1 and R2 to be within 0.1% of ideal values for a 2400-Hz fosc. A value of R3 that produced a 130 dB notch depth was calculated, and results are shown with it and with several slightly larger R3 values. -90° phase shifts with attenuations from 65 to 130 dB are evident for various R3 values.
| Attenuation, dB | 1 – fosc/fnotch | NOtol = 1 – fosc/fnotch |
| -90 | 0.01% | -0.01% |
| -80 | 0.03% | -0.02% |
| -70 | 0.11% | -0.05% |
| -60 | 0.35% | -0.18% |
| -50 | 1.07% | -0.56% |
Table 1. Variations in the oscillation with respect to the notch frequencies and in R3 values for a -90° phase shift at various Aosc attenuations.
Knowing the values of fosc and Aosc, the value of fnotch can be calculated from Table 1. From this, the values of the capacitors and the resistors R1 and R2 can be calculated from equations (1) and (2). With 0.1% resistors for R1 and R2 and 1% capacitors, fnotch will be kept within a range of the tolerance product Stol = 1 +/- 1.01*1.001 ≈ 1.1% of the intended value. Note that regardless of component tolerances, there is always the option of adding a pot in series with either R1 or R2. The aggregate value of that pot plus resistor should have a range of Stol centered at the equation (2) value. The values and tolerances of R3A and R3B should be selected so that R3 can be adjusted to within Stol – NOtol (see Table 1) of the equation (3) value.
It’s worth noting that with the better-known twin-T notch filter [3], I was unable to meet the phase and attenuation requirements simultaneously by varying only a single resistor value. Even if this were possible, the capacitors in the dual T are conveniently identical, while the twin-T’s requirement of a value ratio of 2 limits capacitor choices. This is also a good time to mention that polystyrene capacitors offer the lowest harmonic distortion [4], with non-metalized polypropylene being a secondary choice.
Establishing oscillation amplitude
Of course, the elephant in the room is what I haven’t yet mentioned—the requirement for establishing an oscillation amplitude. One way of doing this is to parallel the R3 resistor plus pot with a non-linear resistor whose value varies inversely with signal level. Unfortunately, any such non-linearity increases harmonic distortion. So it makes sense to choose a non-linear component designed specifically for low harmonic distortion audio applications. The NE570 (an improved version of the SA571 seen in Figure 1) is a low harmonic distortion compressor/expandor IC intended for audio applications [5]. A block diagram of the part appears in Figure 3.
Figure 3 A block diagram of the function of the SA571 and NE570 compandor IC, curtesy of On Semiconductor.
As can been seen, the part has a “delta G” cell whose current gain is controlled by the capacitively filtered output of the rectifier. The capacitively-coupled inputs to both functions are connected in Figure 1 through resistors I’ve added to reduce the functions’ operating levels. These are driven by the output of the LME49720 op amp U2A. (The op amp provided with the SA571/NE570 is of the 741 type and should not be used in extremely low THD applications. Its output and one end of the 20K resistor R3 can be left unconnected. Its inverting input is connected to that of U2A.) Note the 1.8-V reference which is the unavoidable DC operating voltage of the delta G cell and both inputs of U2A.
The SA571/NE570 are dual parts, and use is made of the secondary unit. Its rectifier capacitor pin is grounded to disable its delta G cell, whose input is floating. The uncommitted side of its R3 is connected to its op amp output to produce a stable 3 VDC source. This source drives the Figure 1 R10 pot to supply a current to the THD trim pin. R10 is adjusted to null out the small amount of 2nd harmonic distortion produced by the delta G cell (and possibly by U2A). I powered the circuit from batteries for portability and added the LEDs to keep fresh 9-V batteries from exceeding the +/- 18 V maximum power supply ratings of the op amp. The SA571’s 30k resistor connecting the op amp inverting inputs to ground is unavoidable. With Figure 1’s R3, it biases that op amp’s output to approximately 4.5 V( (≈45k/30k + 1)*1.8 V ). This level can be reduced by connecting a resistor from the 3-V source to U2A‘s inverting input (not provided in the Figure 1 circuit). With or without this additional resistor, remember to keep a proper DC bias across output electrolytic capacitor C5.
The added passive components at the NE570 inputs are chosen to allow R3 to be adjusted for a 3 Vrms output from U2A, the level at which its datasheet indicates that that op amp exhibits the lowest THD.
Measuring distortion
To measure distortion, I attenuated the oscillator output’s fundamental by running the signal through a second dual T filter with a pot in series with each resistor. By laboriously tweaking each pot in turn, I was able to attenuate the fundamental by 70 dB. The filtered output was applied to an SR770 spectrum analyzer which can accurately measure signals within an 80 dB dynamic range. Tweaking the THD pot to minimize the 2nd harmonic level, I measured the levels of the oscillator harmonics and applied corrections for the filter attenuations at each frequency (see Table 2.) I then took the rms of the levels corrected for the attenuations of the second dual T filter and arrived at a THD more than 130 dB below the oscillator fundamental.
| Harmonic Number | Filter Attenuation, dB |
| 2 | 11.81 |
| 3 | 6.54 |
| 4 | 5.14 |
| 5 | 3.78 |
| 7 | 2.78 |
| 9 | 2.49 |
Table 2 Attenuation of higher harmonics by a dual-T filter tuned as described in the text to maximize attenuation of the oscillator fundamental.
The NE570 and LME49720 datasheets and parts are available online and through DigiKey. Small quantities of the NE570 for experimenters can be had from numerous eBay vendors.
I believe that it’s tough to beat the combination of simplicity and performance afforded by this design and welcome comments from anyone who builds and tests it.
Christopher Paul has worked in various engineering positions in the communications industry for over 40 years.
Related Content
- Getting an audio signal with a THD < 0.0002% made easy
- Measure an amplifier’s THD without external filters
- Ultra-low distortion oscillator, part 2: the real deal
- A simple circuit with an optocoupler creates a “tube” sound
- How to control your impulses—part 2
References
- Paul, C, The Simple Sineman, audioxpress, November 2013, p. 52
- Jung, “Gain Control 1C for Audio Signal Processing,” Ham Radio, 1977, no longer available.
- https://learningaboutelectronics.com/Articles/Notch-filter-calculator.php#answer1
- https://www.tedss.com/LearnMore/Polystyrene-Film-Capacitors offers a wide array of polystyrene capacitors
- ON Semiconductor, NE570 datasheet, https://www.onsemi.com/pdf/datasheet/ne570-d.pdf
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