Is the single-tune Foster-Seeley possible?

created Jun. 2021

Introduction

The Foster-Seeley discriminator requires a transformer that is parallel resonated on both primary and secondary sides; i.e. dual tuning. This rules out using a conventional Intermediate Frequency Transformer (IFT) because only one winding is resonated with an internal capacitor. The dual tuning can be realized by placing two slug-tuned inductors in one shield case, but such component is not commercially available. Hence, there is much interest in adapting the dual-tune Foster-Seeley to single tuning.

This project is motivated by an engineering text which tantalizingly hinted at the possibility of the Foster-Seeley discriminator with 1 tuning element, “requires one or two tuning adjustment” [1]. Additionally, a radio amateur has constructed what is ostensibly a single-tuned Foster-Seeley but did not offer any performance data to validate the design [2].  

Material & method

The prototype utilized 5082-2800 Schottky diodes to demodulate the 10.7 MHz IF signal (fig. 1 & 2). However, the diodes are not critical and can be substituted with silicon small signal diodes such as 1N4148. The tuned transformer utilizes a size 12x7x7 mm IFT that is intended for 10.7 MHz operation - Sumida type S-7GC (fig. 3). The IFT's 4 turn winding is used as the untuned primary, while the 18 turns as the tuned secondary. The secondary is wound over the primary on a bobbin and they share a common tuning slug; i.e. they are very tightly coupled. The 18 turn winding has a centre tap and is parallel resonated with an internal 100 pF capacitor. The primary is coupled to the secondary's centre tap via a capacitor C2. The IFT's tuning slug is adjusted so that the hoped for "s-curve" centers around 10.7 MHz. All measurements are made at the test point marked "Vo". The audio is also taken from this point via DC-blocking capacitor C6. The components are assembled "dead bug" style on a single-sided PCB (fig. 2).

To gain additional insight, the proposed design was modeled in a circuit simulator.  Although simulation of the Foster-Seeley has been demonstrated before, but it was a double-tuned design. Moreover, the aforementioned LTSpice simulation only investigated the demodulated audio (in the time domain) but not the transfer function [3]. However, it is important to study the transfer function in order to prove that the design is capable of generating the desired "s-curve".  If the transfer function is not a s-curve, then the investigated circuit is likely behaving as a slope detector instead of Foster-Seeley discriminator [4]. Another distinguishing characteristic of any FM discriminator is that its s-curve will pass through 0V at midpoint (centre frequency), whereas the slope detector's curve will not (fig. 4).  It is worth recollecting that the Foster-Seeley was first devised for automatic frequency control and the s-curve is essential to this function [5].

In this work,  harmonic balance analysis was used to elucidate the transfer function. The tuned transformer (IFT) was modeled using the XFERTAP component, but a shortcoming of this component is that it did not account for the inductor loss  (fig. 5). The XFERTAP component has two quirks. One, the turn ratio is defined as the primary vs. one half of the secondary; hence, N12 = N13 = (4 turn / 9 turn) = 0.44. Two, only the primary inductance can be specified. The 133.6 nH primary inductance (L1) was arrived at by making the modeled notch frequency (~10.1 MHz) match the measurement (fig. 7). The generator power is 0 dBm in both model and experimental conditions. The demodulated baseband voltage Vo can be taken from either D1 or D2. Taking the output from the bottom node (D2) as shown produces a notch / band-reject response, whereas connecting to the top node (D1) flips the notch response to bandpass.

Results

The coupling capacitor C2 value is not critical. The slope steepness beneficially increases with  C2 capacitance (fig. 6). A final value of 1 nF (-j15 at 10.7 MHz) was chosen because it provided a larger output voltage than either 10 pF or 15 pF . The traces do not cross 0V at their midpoints.

The measured trace follows the straight line (red dashed) over a narrow freq range, 10.6-10.8 MHz (fig. 7). The curve does not cross 0V at its midpoint; i.e. no zero-crossing. Although audio distortion was not measured, it is anticipated that the small linear region will likely distort the output for large deviation. The top and bottom inflections are unsymmetrical. This asymmetry, the lack of zero-crossing and the narrow linear region lend to the suspicion that the observed result is not a "s-curve".

Over the 10.0-11.4 MHz range, the modeled output voltage excursion is 0.80V versus the experimental 0.85V (fig. 8). For unknown reason/s, the modeled trace is erroneously  ~0.5V lower. However, both modeled and experimental exhibit the same shape. 

When the model's frequency range is widened, it shows a notch response centering at 10 MHz (fig. 9). The pale blue region corresponds to the previously evaluated 10.0-11.4 MHz range. Apparently, the previous results are the high side slope of the notch response.  Moreover, the investigated circuit will conceivably respond to signal on its lower slope between 8.5-9.5 MHz, whereas a true discriminator will not exhibit two frequency ranges of detection [4]. This result further reinforces the notion that the achieved demodulation is that of a slope detector.  

Conclusion

The modeled and measured performances do not support the contention that a Foster-Seeley discriminator can be implemented with a single tuning element. Although the evaluated single-tune design can demodulate FM and produce audio, it is likely working as a slope detector instead of as a Foster-Seeley discriminator. 

References

[1] P. Vizmuller, RF design guide, Artech, 1995. pp. 89. 

[2] A. Yates, "FM Detection Experiments", May 2007, http://www.vk2zay.net/article/119

[3] A. Scher, "Foster-Seeley FM Detectors". http://aaronscher.com/Circuit_a_Day/week_by_week/August_2016_FM_Foster_Seeley_detector/FM_Foster_Seeley_Detector.html

[4] R. Weaver, "FM Crystal - slope detector question", The radio board forums, 4 Jun. 2014,  http://www.theradioboard.com/rb/viewtopic.php?t=5685#p51928

[5] D. E. Foster & S. W. Seeley, "Automatic Tuning, Simplified Circuits and Design Practice," Proc. Inst. Radio Engineers, vol. 25, no. 3, Mar. 1937

Update: 11 Jul. 2021

The transformer in the double-tuned Foster-Seeley discriminator has a low coupling coefficient [3]. Returning to the goal of devising a single-tuned discriminator, if the primary-secondary coupling is reduced to ~0.3, then the transfer function changes to a correct s-curve with zero crossing (fig. 10 & 11). Through this hack, a single-tuned Foster-Seeley can be potentially realized. The downside is the output amplitude is several times lower than a conventional double-tuned Foster-Seeley. However, the convenience / economy of single tuning may make the lower output a worthy trade-off.

To the reduce the transformer coupling coefficient, its two coils must be physically spaced some distance apart. One way to realize the low-k transformer is to wind the coils on opposite ends of the bobbin - like the valve-era double-tuned IFT (fig. 12). Unfortunately, the manufacture of the double-tuned IFTs have ceased decades ago. So, the single-tuned diode discriminator will remain a dream for many experimenters!

Related article: Getting an s-curve from the Foster-Seeley discriminator