NPN Sziklai pair small-signal amplifier for high gain low noise submicron voltage recorder

Received Jul 20, 2021 Revised Jan 12, 2022 Accepted Jan 28, 2022 Small signal-to-noise ratio (SNR) and multiple noise sources, coupled with very weak signal amplitudes of bio signals make brain-computer interface (BCI) application studies a challenging task. The front-end recorder amplifiers receive very-weak signal (few μV) from high impedance electrodes and for efficient processing of such weak and low frequency (<1 kHz) signals a high gain amplifier with very low operating voltage and low total harmonic distortion (THD) is required. Existing amplifiers suffer from problem of high non-linearity and low common mode rejection. A good sense amplifier at predeceasing stage can solve this problem. Utilizing very high amplification factor of Sziklai Pair, this paper proposes two circuit topologies of common-emitter and common-collector negative-positivenegative (NPN) Sziklai Pair small signal amplifiers suitable for use in preamplifier stages of such signal acquisition circuit. Present study provides broad-spectrum of analysis of these amplifiers covering effect of additional biasing resistance RA, variation of ‘ideal forward maximum beta’ β, temperature dependency, noise sensitivity and phase variation. The tunable capability of first topology makes it a suitable candidate in wide variety of other applications. The first amplifier operates on very low input voltage range (0.1 μV-6 mV) whereas the second amplifier works on 100 μV-11 mV range of input voltage.


INTRODUCTION
Low frequency small signal voltage measurement in submicron region (<1 µm) is a challenging task especially with noisy, non-stationary sources such as bio-signals. Correct measurement with very high gain, high sensitivity amplifiers is the key to reliable results [1]. There is a practical limit to gain of available semiconductor devices for amplifier design and it forces use of multi stage design for high gain. Multistage amplifiers not only occupy large area but also suffer from low noise immunity and high harmonic distortion. Various attempts have been made in past to increase device gain such as use of Darlington pair and Sziklai pair in place of bipolar-junction-transistor (BJT). Sziklai offer lower turn on voltage but its performance depends greatly on matched parameters of used pair of transistors. There is not much reported work available on circuit arrangement and amplifier based on these device configurations [2]. This paper deals with novel arrangement of negative-positive-negative (NPN) Sziklai pair amplifier with varying biasing arrangement and matched BJT pair combination under common-emitter (CE) and common-collector (CC) configurations [3]. CE amplifiers are most common fundamental amplifying circuit that produces undistorted output as long as the small-signal base-emitter voltage (vbe) is less than thermal  [4]. Emitter resistance RE provides negative feedback which enhances current gain and reduces distortions in the amplified output with 180 0 phase shift [5]. Conventionally, CE amplifiers have wide application in audio amplifiers, basic switch for logic circuits, general analog amplifiers, speakers, microcontrollers and DC motors due to moderate voltage and current gain with moderate input and output impedances [6]. The CC amplifiers produces nearly unit voltage gain, high current gain. Its output emitter voltage follows input base voltage, and the input impedance is much higher than output impedance [7]. CC amplifier is frequently employed as a voltage buffer and used for impedance matching [8]. CC amplifiers have relatively better frequency response and less distortion in comparison to CE and Common-Base (CB) amplifiers [9].
Sziklai pair, named after its Hungarian inventor George Sziklai, works as high gain amplifier similar to Darlington pair but it requires only half turn-ON base-emitter voltage (VBE=0.625 volt) than Darlington pair (VBE=1.36 Volts) [10]. A major advantage associated with Sziklai pair small-signal amplifiers is that it has better response at higher frequencies than Darlington pair small-signal amplifiers [11]. At higher frequencies the matched Sziklai pair device current gain is β 2 whereas for unmatched Sziklai pair it is β 1 × β 2 [12]. The lower quiescent current makes Sziklai pair thermally stable than Darlington pair and also shows better linearity [13]. This paper covers detailed analysis of NPN Sziklai pair small-signal amplifiers under CE and CC configurations with matched pair of BJTs. Two circuit topologies proposed in this paper overcome the narrow bandwidth problem of PNP Sziklai pair small-signal amplifier and also removes the poor response problem of conventional Darlington pair small-signal pair amplifier at higher frequencies [14].

CIRCUIT DESCRIPTION AND RESEARCH METHOD
Two circuit topologies, proposed in this paper, are the circuit models of NPN Sziklai pair smallsignal amplifier. Circuit-1 amplifier under the CE configuration is shown in Figure 1 (a) and circuit-2 amplifier under the CC configuration is shown in Figure 1   NPN Sziklai pair small-signal amplifier for high gain low noise submicron … (Sachchida Nand Shukla)

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As the designed amplifier circuits use NPN-type transistor at driver position and PNP-type transistor at follower position, hence it is termed as NPN-type Sziklai pair small-signal amplifier. Device structure of the CE amplifier operates with base voltage 9.1789 V at node 3 and 8.8499 V at node 5 whereas for CC amplifier it works with base voltage 6.6306 V at node 3 and 12.8820 V volt at node 7. Table 1 and Table 2 lists all the simulation parameters used in modeling of transistors and the operating point.

Effect of additional biasing resistance RA on circuit-1
Performance parameters of circuit-1 amplifier are greatly affected by additional biasing resistance RA, whose value is 200 K in Case-A1 and 100 K in Case-B1. In addition to RA the value of R1 is decreased to 90 K from 95 K in Case-A1 and 85 K from 90 K in Case-B1, to maintain bias point at node 3, keeping other circuital parameters unaltered. Table 4 lists the performance parameters of these amplifiers under effect of RA. Increment in the base-collector voltage of follower transistor in Sziklai pair combination, from 0.3 V-1.22 V, results in significant improvement of the performance parameters of both the amplifiers with increased THD (2.06%).

Effect of biasing resistors R1 and R2 on circuit-2
Effect of biasing resistors R1 and R2 on the performance of circuit-2 has also been figured out. It has been found that biasing resistors R1 and R2 has significant impact on the performance parameters of the circuit-2. Optimum performance of circuit-2 is reported when their values are high (Mega ohm). However, biasing resistors at R1=25 MΩ and R2=50 MΩ gives very high THD (46.78%) however the device voltage gain AVGD gets distorted giving lesser power gain [19].
THD of all the amplifiers fluctuate with the range of AC input signal whereas all the other performance parameters remain mostly unaltered. Lowest value of THD for the amplifier under Common-Emitter and Common-Collector configuration is received at the range (0-1 µV, 1 KHz) and (0-1 mV, 1 KHz) respectively. It has also been found that Fourier analysis is aborted at the range (0-10 V, 1 KHz) of the amplifier circuit-1 and (0-100 V, 100 KHz) range of Case-A1 and circuit-2.

Effect of capacitors
The distortion of the waveform in the output signal is found to be a very serious problem in BJT based common-emitter and common-collector amplifiers at higher frequencies [20]. It has been observed that bypass capacitor CE and load capacitor CL play a very significant role in minimizing this problem. Variation of total harmonic distortion (THD) with respect to bypass capacitor CE for circuit-1, Case-A1 and Case-B1 and load capacitor CL for circuit-2, Case-A2 and Case-B2 has been observed. It has been found that THD of circuit-1 increases to CE=100 nF. From CE=100 nF to CE =10 uF, THD fluctuates and tends to saturation at higher values of CE (e.g., CE ≥100 uF). Similarly, for case-A1 and case-B1, THD peaks at 100 nF and decreases beyond this value. Similarly, THD of circuit-2 remain almost constant up to CL=100 nF. It must be noted that CL is an essential component for the Circuit-2. When it is detached from circuit-2, amplifier current gain increases to 1,559.8 and total harmonic distortion decreases to 0.7% (worth noting that the combination device current gain AIGD remains unaltered).

Tuning performance of circuit-1
Tuning performance of the amplifier is studied by varying emitter bypass capacitor CE under no load condition (CL removed) and under varying load (CL) keeping emitter bypass capacitor CE fixed at 100 uF under constant biasing condition [21]. Tuning with CE and CL is received for the variation between 10 nF-100 mF and 1 fF-10 nF. Amplifier voltage gain and amplifier current gain remains almost constant for any variation in CE whereas FL decreases from KHz to Hz range and FH remains unchanged on increasing CE. Similarly, tuning performance with CL is obtained for the variation between 1 fF to 10 nF. Increment in CL causes FH to shrink from MHz to KHz range whereas voltage gain and current gain remains unchanged.
Tuned frequency response of the circuit-1 has been drawn in Figure 3 under two different combination of tuning capacitor, first with CE=100 uF and CL=10 pF and second with CE=50 uF and CL=1 pF which is referring to the fact that proposed amplifier can be used to obtained desired frequency of a specific channel by the proper adjustment of CE and CL.

Range for biasing components of circuit-1
It has been found that variation in base resistance RS does not affect amplifier current gain AIGA whereas amplifier voltage gain AVGA decreases with increasing RS. Minimum value of amplifier voltage gain AVGA is received at RS=1.3 MΩ (AVG-MIN=1.0507) and maximum value at RS=1 Ω (AVG-MAX=48.453) with meaningful amplification in 1 Ω≤RS≤1.3 MΩ range. Similarly, AIGA and AVGA both decreases with rising value of collector resistance RC up to a critical limit 9 KΩ but beyond this critical limit, response curve of both AIGA and AVGA distorted badly. Maximum value of AVGA is received at RC=9 KΩ (AVGA-MAX=48.453) and minimum value at RC=16 Ω (AVGA-MIN=1.0348) with faithful amplification range 16 Ω≤RC≤9 KΩ whereas Maximum value of AIGA is received at RC=9 KΩ (AIGA-MAX=1,746.5) and minimum value at RC=1Ω (AIGA-MIN=2.3753) with purposeful amplification range 1 Ω≤RC≤9 KΩ. It is worth noting that the proposed amplifier switches-ON at 2 V DC supply voltage. Amplifier voltage gain AVGA gives distortion-less responses in 2 V-35 V range of VCC whereas amplifier current gain AIGA gives distortion-less responses in 2-60 V range of VCC. Both AIGA and AVGA rises gradually up to 30 V and falls linearly beyond this value. It is also to be noted that increment in load resistance RL causes corresponding increase in AVGA and simultaneous decrease in AIGA. Therefore, Minimum value of AVGA is achieved at RL=16 Ω (AVGA-MIN=1.0535) but beyond this value it gradually rises and becomes saturated at RL=7 MΩ (AVGA= 591.068) whereas maximum value of AIGA is received at RL=1 Ω (AIGA-MAX=1902.3) and minimum value at RL=17 MΩ (AIGA-MIN=1.0013) with purposeful amplification range 1 Ω≤RC≤17 Ω.

Effect of β variation on overall performance of proposed amplifier
Modelling of β is important for small-signal amplifiers based hence observations are recorded for range of 'ideal maximum forward beta' β in the modelled BJTs [22]. Although the theoretical gain of such combination is the product of current gains of constituent BJTs but practical gain is always lower due to secondary effects. The overall device gain of such pair also depends on the arrangement of stage gain as leakage and bypass currents also get amplified at later stage. This section covers detailed simulation analysis of impact of stage gain and their order on overall device gain along with frequency response.

Effect of β variation on the circuit-1
Performance parameters of circuit-1 at identical values of: i) β, ii) fixed β1 and varying β2, and iii) fixed β2 and varying β1 has been studied. It has been observed that at identical values of β, AIGA, AVGA, AVGD and AIGD increases and bandwidth decreases with increasing β1 and β2, however THD remains constant at 0.9%. Variation of AIGA and AIGD with frequency at identical β values is illustrated in Figures 4 (a) and 4 (b). It has been observed that amplifier current gain remains constant at mid frequency ranges extended from 1KHz to 1 MHz and decreases at higher (≤ 1 ) and lower frequency ranges (≤ 1 ) whereas device current gain remains constant at 1 Hz to 100 KHz frequency range and decreases at higher frequency ranges (≤ 100 ). As a usual feature of small-signal amplifier, performance parameters of the proposed amplifier increase with rising values of like and unlike 1 2 which authenticate the proposed amplifier.  When β2 is fixed at 250 and β1 is varied up to 250, AIGA, AVGA, device voltage gain AVGD and AIGD increases whereas THD remains constant at 0.9%. However, bandwidth undergoes sharp decrement at β1=100 β2=250. As per % variation of AIGD reported, ideal response of the amplifier is achieved at β1=5 and β2=250. Similarly, when β1 is fixed at 250 and β2 is varied up to 250, increment in AIGA, AVGA, AVGD, AIGD and bandwidth is observed whereas THD remains constant at 0.9%. Ideal behavior of the proposed amplifier under this condition is achieved at β1=250, β2=5 and β1=250, β2=25. The proposed amplifier shows idealistic behavior at lower values of both β1 and β2. Increasing the range of β1 and β2 causes corresponding decrease in bandwidth [23].

Effect of β variation on the circuit-2
Performance parameters of the circuit-2 with different values of β has also been observed. Circuit-2 works well up to β1=β2=50 with high AIGA (1,202.8) and low THD (1.87%) but beyond this value, this amplifier suffers from Higher THD, consequently could not retain the status of matched Sziklai pair smallsignal amplifier. Moreover, maximum amplifier current gain AIGA-MAX is obtained at β1=β2=75 but due to high level of distortion, this condition could not be taken under consideration for matched pair of BJTs for the proposed amplifier. The optimum performances with matched pair of BJTs is obtained at values of β1 and β2 below 50.
When β1 is fixed at 50 and β2 is varied up to 100, all the performance parameters increase with increasing range of β except THD which becomes higher at lower value of β2 and lower at higher value of β2 keeping β1 fixed at 50. This also refers that proposed amplifier gives acceptable performance with unmatched pair of BJTs. Ideal behavior of the proposed amplifier under this condition is obtained with unmatched pair of BJTs under the condition β1=50 β2=2, β1=50 β2=20 and β1=50 β2=30. Similarly, when, β2 is fixed at 50 and β1 is varied up to 100, all the performance parameters increase with increasing range of β Variation of AIGA and AIGD with frequency at equal values of β is shown in Figures 5 (a) and 5(b). Proposed amplifier gives 'Maximum Amplifier current gain' AIGA-MAX at β1=β2=50 and 'Minimum Amplifier current gain at AIGA-MIN at β1=β2=100. Similarly, 'Maximum Device current gain' AIGD-MAX is obtained at β1=β2=50 and 'Minimum Device current gain AIGD-MIN is obtained at β1=β2=100. The overall result show that β1 and β2 are not to be kept above 50 for the circuit-2 to act as matched Sziklai pair small-signal amplifier. Also, the amplifier in discussion provides ideal behavior for both the β below 50.

Temperature variation
Temperature dependency of the circuit-1 and circuit-2 has also been studied [24]. It has been found that all the performance parameters of the circuit-1 decrease with rise in temperature except bandwidth which increases up to −10 ℃ undergoes sudden decrement at 0 ℃ which further attain rising trend at higher temperatures. This happens due to the fact that base-collector voltage of second BJT decreases with increasing temperature which causes decrement in collector current which in turns reduces current gain and voltage gain.
Similarly, in circuit-2, no significant impact of temperature is reported on device current gain AIGD and AVGA. However, AIGA, AVGD decreases and THD increases initially and thereafter decreases beyond. This shows that proposed amplifier is thermally stable over the wide range of temperature -30 °C≤T≤50 °C. Possible reason for such behavior is that when temperature is increased within the range -30 °C≤T≤50 °C, base-collector voltage of second transistor VBC drops from 6.96-6.87 V which causes reduction in collector voltage VC which results in the lowering of AIGA & AVGD.

Noise sensitivity
Noise analysis of the circuit-1 at 100 Hz, 1 KHz, 10 KHz, 1 MHz and 100 MHz frequencies and circuit-2 at 10 Hz, 100 Hz, 1 KHz, 100 KHz and 1 MHz frequencies with respect to temperature has also been observed [25]. It has been found that input noise of the circuit-1 increases with rise in temperature whereas output noise increases with temperature elevation at 100 Hz and 100 MHz frequencies. But, at 1 KHz, 10 KHz and 1 MHz operating frequencies, it increases up to room temperature (27 ℃) but decreases beyond this value. It has also been observed that input noise remains constant up to 10MHz frequency and thereafter increases exponentially whereas output noise remains constant over the frequency range 1 KHz to 100 KHz and deceases at higher (≤ 100 ) and lower frequency (≤ 1 ). Similarly, both input and output noise of circuit-2 increase with rise in temperature which demonstrates the usual feature of small-signal amplifier. It is noteworthy that at 10 Hz,100 Hz and 1 KHz frequency, range of both input and output noises are equal to each other (range 10 -9 V/Hz) whereas range of input noise (10 -9 V/Hz) become greater than range of output noise (10 -12 V/Hz) at 100 KHz and 1 MHz frequency ranges [26].

Phase variation
The phase-frequency response allows us to see exactly how the output gain and phase changes at a particular point over range of different frequencies [27]. Simulated responses of Phase-frequency variation of output current to input current for proposed amplifiers has been observed . It has been found that under the Sziklai CE-configuration, phase variation of circuit-1 and Case-A1 decreases with frequency elevation whereas in Case-B1, phase variation decreases up to 10 MHz frequency and increases beyond this value. Similarly, under Sziklai CC-configuration, phase variation of Case-A2 and Case-B2 decreases up to 1 MHz frequency and increases beyond this limit whereas in Circuit-2, it decreases with simultaneous rise in frequency [28].
Analysis of the equivalent circuit of Figure 6 provides the expression for the AC voltage gain of the proposed amplifier as, and the expression for the AC Current gain can be obtained as equal to, (1 + 2 ) ] Figure 6. Small signal AC equivalent circuit of circuit-1

CONCLUSION
Sziklai compound pair are often used in output stages and also in areas requiring very high current gain with smaller drive voltage. Present paper covers a detailed analysis of Sziklai Pair as device with varying component characteristics along with NPN Sziklai pair small-signal amplifier under CE and CC mode using matched pair of BJTs. Proposed amplifiers removes the narrow-bandwidth problem of PNP driven Sziklai pair small-signal amplifier and poor response problem of Darlington pair small-signal amplifiers at higher frequencies. It has also been found that at 1 KHz of operating frequency, circuit-1 shows better noise performance than that of circuit-2. Moreover, phase difference of output-to-input current in circuit-1 is lower in comparison to circuit-2. Proposed amplifiers are capable of amplifying 0.1 µV-6 mV and 100µV-11mV range of AC input signal at 1KHz frequency respectively.
The circuit-1 performance parameters are improved in the presence of additional biasing resistance RA with elevtaed THD, however it limits faithful current amplification in the range 2-60 V of DC supply voltage at room temperature along with excellent thermal stability over the operational temperature range -30 °C≤T≤50 °C. At lower values of β (β≤50), this amplifier is also found to exhibit ideal behavior with narrow bandwidth. Similarly, Circuit-2 amplifier produces higher current gain with strong dependency on R1 and R2. It has been found that this amplifier works well as the matched pair of BJTs up to β1=β2=50 but beyond this value, this amplifier suffers from higher THD, consequently could not retain the status of matched Sziklai pair small-signal amplifier. This amplifier gives considerable responses at R ≥9 KΩ and RP≤20 KΩ and the high margin between the output-to-input current and output-to-input voltage in transient and AC analysis in circuit-2 can be justified as it is a Sziklai pair small-signal amplifier under commoncollector configuration.
Present study covers a broad-spectrum of analysis of proposed two amplifiers configurations including effect of biasing resistance RA, variation of 'ideal forward maximum beta' β, temperature dependency, noise sensitivity and phase variation. First amplifier configuration circuit-1 operates on very low input voltage range (0.1µV-6 mV) and gives high current gain (1,746.5), high amplifier voltage gain (48.453), wider bandwidth (3.1976 MHz) and low THD (0.9%). The second amplifier configuration circuit-2 works on input voltage range of 100 µV-11 mV and gives undistorted output with high current gain (1,202.8), nearly unity voltage gain (0.958) for signals below 383.728 Hz.