Voltage followers for the design of Sallen-Key Active RC-Filters

: In this paper consider the circuitry of voltage followers (VF) with unity-gain, intended for practical use in active Sallen-Key RC-filters (LPF, HPF, BPF, RF). The results of research and computer modeling of radiation-resistant and low-temperature VF in the LTSpice environment on models of CJFET transistors operating under the influence of neutron flux up to 10e14 n/cm2 and cryogenic temperatures up to -197°C are presented.


Introduction
The active RC-filters (ARCF) of Sallen-Key family are among the most popular devices in frequency selection for radio engineering, automation and telecommunications [1]. As amplifying elements in ARCF of this class used operational amplifiers with 100% negative feedback [2] or buffer amplifiers (BA), which implemented on one or several transistors (BJT, CMOS, SOI, etc.). In recent years this area of practical application of the Sallen-Key ARCF family has emerged as an independent subclass of frequency selection devices [3][4] including for work in severe operating conditions. Practical realization of Sallen-Key filters family on voltage followers (VF) has, in contrast to ARCF Sallen-Key on operational amplifiers (OPA), an important advantage -VF circuits can be performed in the form of the simplest emitter or source followers [5][6][7][8][9][10]. As a result, such ARCF active elements are distinguished by a wider operating frequency range and low power consumption in comparison with OPA.
The purpose and novelty of this article is to consider the circuitry of voltage followers and their practical use for Sallen-Key ARCF family, including those operating at low temperatures and a neutron flux.
Below are the basic equations of Sallen-Key ARCF that allow you to choose their settings [11]. So, for the low-pass filter circuit (Figure 1 (a)) the transfer function is determined by the expression The transfer function of the high-pass filter (Figure 1 and pole frequency . In the band-pass filter circuit (Figure 1 (c)), the transfer function is determined at that pole attenuation and pole frequency . Figure 2 shows examples of the inclusion of a VF [16] in the structures of a 3rd order Chebyshev low-pass filter (LPF) (Figure 2 (a)), in a 4th order Butteworth LPF (Figure 2 (b)), in a 5th order Bessel LPF (Figure 2 (c)). In a particular case, as buffer amplifiers BA1 and BA2 in the circuit on Figure 2 (c) may be using on op amps with 100% negative feedback can be used.

The Voltage Follower Circuits for Sallen-Key Active RC-Filters
The analysis of the VF circuitry, which are used in Sallen-Key ARCF family [1][2][3][4], shows that for these tasks the circuits are used, shown on Figure 3. The voltage followers on Figure 3 (a) and Figure 3 (b) are among the most widespread. Their properties are studied in detail in monographs on analog circuitry [16][17]. The flaw of these circuit solutions is a rather large systematic component of the zero bias voltage (V off ), which is determined by the emitter-base (gate-source) voltage of the used transistors. In VF based on composite transistors (Figure 4 (a), (b), (c)), the difference between the input and output static voltages can be quite small. This is provided by the circuitry of the voltage followers, the topology of the transistors and the applied technological processes. Construction of VF for the Sallen-Key ARCF family is possible on the basis of the circuitry on simplest OPA with 100% negative feedback ( Figure 5), which allows us to reduce V off . However, the frequency characteristics of such voltage followers will be somewhat worse than in control units without feedback. On Figure 5 presented CM1 is a current mirror. To obtain the limiting parameters of the Sallen-Key ARCF family in the frequency range, special VF are designed, including those operating in severe operating conditions [11].

Low-temperature and radiation-resistant voltage follower on complementary field-effect transistors with a control p-n junction
In Figure 6 and Figure 7 shows two proposed [18][19] circuit modifications of the VF with small V off , which made on complementary field-effect transistors with a control pn-junction and provide a low noise level, including when operating in the low temperature range.  Consider the work of the VF (Figure 7) taking into account the results of modeling its characteristics shown in Figure 8 - Figure 12. In static mode, with a large load resistance R load , the source currents of the output and input field-effect transistors J3, J2, as well as the input and output field-effect transistors J1, J4 are determined by the formulas where R 1 , R 2 are the resistances of the corresponding current-stabilizing resistors R1, R2; V GS.i is the gate-source voltage of the i-th field-effect transistor at a given source current.
From formulas (4) and (5) it follows that the static modes of the input fieldeffect transistors J1, J2 can be set independently of each other by currentstabilizing resistors R1, R2. In this case, the static voltage at the output of the VF (with identical drain-gate characteristics of transistors with p-and n-channels) is close to zero: In practical VF circuits, due to the difference in threshold voltages of transistors with p-and n-channels in the circuit in Figure 7, the output voltage (the so-called zero bias voltage VF V off ) lies in the ranges of units to tens of millivolts.
In this case, the numerical values of V off can be set, depending on the range of external influences, due to the rational choice of resistances R 1 and R 2 .
If the input voltage in the circuit (Figure 7) receives a positive increment, then the current in the load R load also receives a positive increment due to an increase in the source current of the output field-effect transistor J3.
At negative input voltages, the increase in current in the load is provided by increasing the source current of the output field-effect transistor J4.
In Figure 8 shows the static mode of the VF (Figure 7) in LTSpice CAD at t=27ᵒC (Figure 8 (a)) and at t =-197ᵒC (Figure 8 (b)). In this case, the computer models of JFET transistors presented in [19] were used. In Figure 9 shows the dependence of the output voltage (V out ) on the input voltage (V In ) VF (Figure 8 (a)) at t=27°C and different load resistances (R load =5kOhm/10kOhm/20kOhm/50kOhm/500kOhm/∞). In Figure 10 shows the dependence of the output voltage (V out ) on the input voltage (V In ) VF on (Figure 8 (b)) at t=-197°C and different load resistances (R load =5kOhm/10kOhm/20kOhm/50kOhm/500kOhm/∞). As follows from the graphs on Figure 9 and Figure 10, the proposed voltage follower provides (at large load resistances R load ) maximum output voltages close to the voltages on the positive and negative power supply rails, incl. in the cryogenic temperature range (Figure 11).
In Figure 11 shows the dependence of the output voltage of the VF (Figure 8) on temperature in the range of -197°С ÷ + 27°С at zero input voltage (V in = 0V) and load resistance R load = ∞. Figure 11. Dependence of the output voltage of the VF on temperature.
In Figure 12 shows the dependence of the output voltage of the VF (Figure 8) from the neutron flux in the range Fn=1e13÷1e15 n/cm2 at zero input voltage (V In =0V) and load resistance R load =∞. From the graphs in Figure 11 it follows that the proposed VF circuit is efficient in a wide range of changes in the neutron flux.

Conclusion
The main circuits of voltage follower for Sallen-Key active RC-filters family are considered. Computer simulation shows that the proposed versions of the CJFET VF construction can find application in low-temperature and radiationresistant analog devices [20]. At the same time, due to the appropriate choice of frequency-setting resistors and capacitors in the above-mentioned ARCF circuits, various amplitude-frequency characteristics are realized (Chebyshev, Butterworth and Bessel filters).
Funding: The research has been carried out at the expense of the Grant of the Russian Science Foundation (project No. 18-79-10109-P).

Conflicts of Interest:
The author declares no conflict of interest.