What simulation of the Foster-Seeley discriminator can reveal

Created: 22 Jul. 2021

Update: 14 Aug. 2021. This article has been published in Academia Letters

Introduction

The Foster-Seeley discriminator was originally developed for automatic frequency control which exploits the property of its transfer function - the s-curve [1]. Like its predecessor, the Travis / balanced discriminator, the Foster-Seeley requires two resonant tanks. However, unlike the balanced discriminator’s dual tanks which must be tuned to slightly different frequencies, the Foster-Seeley’s tanks are conveniently tuned to the same frequency; i.e. the Foster-Seeley is an improvement on its predecessor [2]. Nowadays, the double-tuned Foster-Seeley has been almost completely supplanted by the single-tuned quadrature discriminator in commercial designs. However, the Foster-Seeley is irreplaceable in minimalist radio designs due to its low active component count consisting of two diodes, as opposed to the multi-transistor quadrature discriminator.

The Foster-Seeley discriminator requires a double tuned transformer; one that is parallel resonated on both primary and secondary sides. The dual tuned transformer is typically implemented by winding two coils on one bobbin. The spacing between the two coils determines the coupling coefficient which is an important parameter to proper functioning (fig. 1). The coils are tuned by slugs which can be individually accessed from top and bottom, respectively. The slugs are usually ferrite which has the effect of increasing the inductances.

By the time PC-based circuit simulators appeared in the 90s, the Foster-Seeley has already faded from use and from engineering consciousness. Hence, it is conceivable that very few simulations of the Foster-Seeley have ever been carried out. Simulation of the Foster-Seeley can help understanding by visualizing the various components’ function. Moreover, component parameters that are either difficult or tedious to manipulate on a physical circuit, such as the primary-secondary coupling, can be easily varied in the circuit simulator. Although one Foster-Seeley simulation has been demonstrated before, it only evaluated the demodulated audio in the time domain [3]. However, without simulating the s-curve, which is in the frequency domain, it is not possible to know what the zero crossing frequency is or what the discriminator’s sensitivity and linearity performances are. Without knowing these parameters, one cannot determine whether the component values are optimum or not. To simulate the s-curve, we performed a frequency domain simulation on the Foster-Seeley discriminator. To our knowledge, this work is the first ever simulation of the Foster-Seeley’s transfer function in the frequency-domain. This article details the equivalent circuit model used in the simulation and the results obtained.

Material & method

To enable simulation of transfer function, we utilized the circuit simulator’s harmonic balance engine. We elected to reuse the design previously simulated by Scher because it is well documented and the prior result could serve as comparison to our own. The said design operates at 10.7 MHz as is typical of those used in FM broadcast radios. In the simulation circuit, the IF signal is supplied by a generator (PORT1) with a 10.7 MHz nominal frequency (fig. 2). The generator impedance is set to 5 kOhm to replicate the output impedance of the IF amp. The transformer primary L1 combines with C1 to resonate at 10.7 MHz. The secondary windings L2 & L3 form a resonant circuit with C2. Since L2 & L3 are actually one coil with a centre tap, their coupling factor (k) approaches 1. Hence, the combined secondary inductance is Lsec = L2 + L3 + 2k√(L2 x L3) ≈ 17.6 uH. Resistor R4 represents the secondary coil’s loss. Although Schottky diodes are used in D1 & D2,  the choice of diodes is not critical.  

The simulation will focus on the adjustment of three components that are critical to proper functioning. To facilitate understanding, we will begin with the most easily understood component first and then move on to progressively less obvious ones.

We also investigated whether the said prior art could be further optimized. An engineering text specified two conditions for optimum sensitivity versus linearity: k. Qsec = 1.5 and Lsec / L1 = 1.77, where Qsec is the secondary loaded Q [4]. To satisfy the first condition, the simulation’s R4 resistance is reduced to 5k, then for the second condition, L1 is reduced to 9.9 uH. To compensate for the reduced L1 value, C1 is increased to 22.5 pF, so that the 10.7 MHz resonant frequency is maintained.

Results

Tuning the Foster-Seeley discriminator is not as straightforward as tuning an ordinary IFT as the conventional wisdom of “tune for maximum output amplitude”  will not lead to optimal performances. Instead, the results will need to be graphed before the optimal component value can be deduced.

Correct adjustment of the primary resonant tank results in the s-curve having symmetrical top & bottom halves. Although, IFTs are universally adjusted by slug tuning, for ease of simulation, we chose to vary the capacitance instead. Anyway, adjusting either component will yield similar results. When C1 = 12.6 pF, which combines with L1 to resonate at the frequency of 10.7 MHz, the s-curve’s top and bottom excursions are of equal amplitude (fig. 3, blue trace). The other two C1 values, 6.6 pF & 18.6 pF, represent off-tuning the primary to above and below 10.7 MHz, respectively. The latter two capacitances have s-curves with unequal halves. Moreover, their s-curves have reduced linear (straight line) segments compared to the correctly tuned case. Quite unexpectedly, the zero crossing frequency is unchanged for the three capacitance values; hence, the zero-crossing frequency cannot be used as a tuning indicator.

In contrast to primary tuning, secondary tuning can shift the zero crossing frequency. When C2 = 13.3 pF, the zero crossing is at 10.7 MHz (fig. 4, blue trace). The other two capacitance values of 14.3 pF and 12.3 pF result in the zero crossing being wrongly positioned below and above the target frequency, respectively. Hence, one can rely on output voltage measurement to guide the secondary tuning.

The separation between primary and secondary coils can be adjusted to trade-off between sensitivity and linearity. When the coils are loosely coupled, e.g. k=0.1, the s-curve is steepest but has the shortest linear segment (fig. 5, red trace). As coupling tighten, the slope gradually flattens, and the linear segment widens. So, k = 0.3 represents a good balance of sensitivity and low distortion.

Compared to the Scher design, the optimized one has a gentler slope and is linear over a wider bandwidth (fig. 6, red trace). However, we don’t feel the improved linearity is useful in practice because broadcast’s peak deviation is typically limited to 75 kHz.

Conclusion

Simulating the Foster-Seeley’s transfer function - the s-curve - can provide more insight than simulating the demodulated audio in the time-domain. It can identify the parameter that must be monitored during alignment. It also enables tuning of a parameter that is difficult to adjust empirically, e.g. coupling coefficient. Different designs’ sensitivity and linearity can be compared via their simulated s-curves.

References

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

[2] P. Vizmuller, RF design guide, Norwood, MA: Artech, 1995, sect. 2.7.2 FM detectors & modulators

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

[4] P. H. Young, Electronic communication techniques, 4th ed., New Jersey: Prentice-Hall, 1999, pp. 356.