# Design and Analysis of CCII-Based Oscillator with Amplitude Stabilization Employing Optocouplers for Linear Voltage Control of the Output Frequency

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- (a)
- (b)
- (c)
- the majority of already known solutions provide only inversely proportional square root dependence of the FO on the driving force (value of the single resistor, FO~R
^{−1/2}), which limits the tunability to be quite narrow, - (d)
- solutions combining control by value of passive element (or its replacement) and active parameter (for the CO control, for example) are not studied (only Reference [14] discusses the adjustment of the CO by an active parameter; however, the FO is also tuned by an active parameter (R
_{X})), - (e)
- solutions implementing two parameters for FO tuning (completely uncoupled from the CO) in order to extend tunability are not proposed (with the exception of Reference [14], where this operation was not verified),
- (f)
- the simple implementation of necessary systems for amplitude gain control circuit (AGC) for amplitude stabilization utilizing electronically (voltage) controlled CO by a specific active parameter is not considered in the majority of solutions summarized in Table 1. Therefore, many topologies have very uncomfortable CO (with a typical form of C
_{1}= C_{2}or R_{1}= R_{2}, and their presence is also found in the FO as product of R_{1}R_{2}and C_{1}C_{2}, see for example solutions in [17,18]). An additional active or passive parameter suitable for the adjustment of CO (not included in the FO relation) should be included, but it cannot be revealed (in these simple solutions having 2 R, 2 C) without the analysis of general (not equal to unity) terminal transfer relations of the active elements (current conveyors).

## 2. Detailed Qualitative Comparison of the Most Similar Solutions and the New Proposal

_{X}) by the bias current. This means that external resistors are not present in the solution [14]. Unfortunately, current conveyors with controllable internal resistance R

_{X}are not available on the market. The control of the bias current (in order to adjust R

_{X}) also has a significant impact on the frequency bandwidth (transfer Y→X), input dynamics, and linearity as well as the output resistance of the current conveyor (unintentional but unavoidable) [20]. Then, the range of R

_{X}value can be very limited. This results in a reduced range of FO tunability. Therefore, our contribution, by solving the tunability of the FO with external replacements of both resistors, brings improvement to the common practice (especially owing to the very low ratio of the driving force vs. the ratio of FO readjustability, see Table 2). The CO in Reference [14] also proposes adjusting by the bias current, setting a gain between the X and Z terminals of the current conveyor. Unfortunately, the implementation of the topology as a two-phase oscillator as well as the analysis of the output relation has not been performed and only a single-resistance R

_{X}was employed for the FO tuning. This results in an inversely proportional square root dependence of the FO on R

_{X}, i.e., limited tunability. Therefore, the full potential of the topology was not revealed and tested in Reference [14]. A very low output amplitude (only slightly more than 20 mV) was also obtained in the results of Reference [14]. Our solution offers a larger output level (amplitudes more than 100 mV). All these aspects (and more details) are clearly visible in Table 2. Lahiri [17] proposed a very similar (topologically) circuit (Figure 1a in Reference [17]), producing output signals in current form. However, the topology also had high-impedance nodes where the output voltages were presented. Several features, compared in Table 2, are similar to those of Reference [14] and our proposal (number of active and passive elements, character of allowed and tested FO dependence). Nevertheless, the range of tested tunability is very narrow (narrow change of resistance value = low ratio of FO readjustability), CO cannot be electronically controlled, and the generated levels are not independent from the tuning process. Other similar solutions (listed in Table 1) do not provide detailed information about the features required for the comparison in Table 2. Therefore, other solutions are not included in this detailed comparison (Table 2).

## 3. Implementation of Optocouplers for Control of VCO

## 4. Topology Suitable for Selected Method of FO Control

_{Y}= 0, V

_{X}= V

_{Y}—whereas the most important difference rests in the transfer of the current from the X to Z terminals (I

_{Z}= −I

_{X}for CCII− and I

_{Z}= B∙I

_{X}for ECCII+). The parameter B represents a generally adjustable current gain. The characteristic equation of this simple oscillator is:

_{2}/C

_{1}. The most important advantage of the solution results from the mutually independent CO and the FO, completely defined by the values of both capacitors and resistors having the typical form of ω

_{0}= (R

_{1}R

_{2}C

_{1}C

_{2})

^{−1/2}.

_{1}= R

_{2}= R, C

_{1}= C

_{2}= C), the previous relation can be simplified to:

_{1}and R

_{2}simultaneously. Note that the controllability of the FO by a single value (R

_{1}or R

_{2}) causes amplitude and phase shift changes (when the FO is tuned). Valuable engagement of both resistors for the FO control is not a typical feature in such simple circuitries (Figure 1). This represents a very important finding in comparison with standard SRCOs and other solutions [1,3,4,5,6,7,8,9,10,11,12] tunable by a single parameter value only. Moreover, the dependence of the generated output level on the tuning process (variation of the parameter intended for the FO tuning) presents an unwanted secondary effect of the single-parameter controllability of the FO [26]. It brings additional issues with amplitude limitation and distortion. In our case, this was not an issue.

_{p}

_{1}, C

_{p}

_{2}(in parallel to C

_{1}, C

_{2}) and resistances R

_{X}

_{1}, R

_{X}

_{2}of the current input terminals (in X of both current conveyors) are considered:

*****) can be derived from Equation (5a) as follows. The equation for ω

_{0}* (5c) provides the expected values of FO used in Equation (8) and shown in Table 3 when the oscillator is tuned. The relative sensitivity of the FO to the main parameters (R

_{1}, R

_{2}, C

_{1}, C

_{2}), in an ideal case derived from (1), reaches a typical value of −0.5. The sensitivities of the FO, including the effect of important parasitic parameters presented in (5c), are: S

_{R}

_{1}

^{ω0}* = −R

_{1}/[2∙(R

_{1}+ R

_{x}

_{1})], S

_{R}

_{2}

^{ω0}* = −R

_{2}/[2∙(R

_{2}+ R

_{x}

_{2})], S

_{C}

_{1}

^{ω0}* = −C

_{1}/[2∙(C

_{1}+ C

_{p}

_{1})], S

_{C}

_{2}

^{ω0}* = −C

_{2}/[2∙(C

_{2}+ C

_{p}

_{2})], S

_{Rx}

_{1}

^{ω0}* = −R

_{x}

_{1}/[2∙(R

_{1}+ R

_{x}

_{1})], S

_{Rx}

_{2}

^{ω0}* = −R

_{x}

_{2}/[2∙(R

_{2}+ R

_{x}

_{2})], S

_{Cp}

_{1}

^{ω0}* = −C

_{p}

_{1}/[2∙(C

_{1}+ C

_{p}

_{2})]. In fact, these sensitivities have absolute values lower than those of the ideal case (<0.4 numerically for particular values from our design).

_{p}

_{1,2}and R

_{X}

_{1,2}in this case. However, there are solutions where these effects cannot be omitted and full consideration of all parasitic features must be provided for the accurate estimation of behavior at high frequencies and when the value of C

_{1,2}is set in hundreds of pF or lower. The specific values of C

_{p}

_{1,2}for our case are discussed in the next section.

## 5. Design of Oscillator and Results of Experiments

_{1}= C

_{2}= C = 47 pF. Note that this selection (tens of pF) is generally required in combination with resistance values (R

_{1}= R

_{2}= R) in hundreds of Ω for the operation of this and similar oscillators above 1 MHz. However, the values of working capacities are not far from the values of stray capacitances of circuitry including the terminal capacities of active devices (units of pF). The internal value of X terminals of CCIIs (R

_{X}

_{1,2}) must also be taken into account from Equation (5a) and (5c). The current conveyors used in our topology (Figure 1) are established by current-mode multipliers EL2082 [27] and a high-speed single-input single-output transconductance amplifier known also as a diamond transistor OPA615 [28]. The electronically controllable gain B (proportionally driven by V

_{SETB}voltage: B ≅ V

_{SETB}for V

_{SETB}≤ 2 V [27]; because B ≅ k∙V

_{SETB}, where k = 1 [V

^{−1}] is valid for V

_{SETB}≤ 2 V) of EL2082 was set to B = 1 for CCII− operation. The cascade of EL2082 with OPA615 (output inversion of CCII−) creates ECCII+ type where B can be controlled to drive the CO by an external AGC for the amplitude stabilization of the generated waveforms (Figure 2). The main purpose of the AGC consists in the sustentation of unchangeable output levels when the oscillator is tuned. This feature cannot be simply obtained when the CO is set to fulfill an analytically obtained relation because energetic (gain) proportions in the circuit are influenced by tunability. The operation without AGC leads to issues with output waveforms (damage of the shape by nonlinear transfer responses of active devices or even limitation), resulting in high total harmonic distortion (THD) (increased level and amount of higher harmonic components and increased level of spurious combination products) or fading (drop down) of oscillations. Voltage buffers (not included in the simplified schemes), based on the OPA2652 [29] operational amplifier, are added to high-impedance nodes for the impedance separation and subsequent measurement of the circuit on a printed circuit board (PCB) by a low-input-impedance (50 Ω) spectrum analyzer HP4395A and oscilloscope Rigol DS1204B.

_{p}

_{1}= 3 pF and C

_{p}

_{2}= 10 pF (in parallel with C

_{1}and C

_{2}) where C

_{p}

_{1}includes the Y terminal capacity 2 pF (CCII−) [27] and input capacity of voltage buffer (1 pF) [29]. The estimated effect of C

_{p}

_{2}supposes a capacity of 5 pF of the Z terminal (CCII−) [27] and the Y, Z terminals (2 + 2 pF) of ECCII+ [28], as well as the input capacity of the voltage buffer (1 pF). Terminal X has an expected input resistance R

_{X1,2}= 95 Ω [27].

_{1}and R

_{2}values simultaneously by a dual-channel tandem potentiometer. Our design intention targets tunability in the approximate range of 1–10 MHz. The discussed method (potentiometer) is not very comfortable for standard applications. Many systems produce a DC driving voltage or current (after D/A conversion). Therefore, we seek useful methods of indirect electronic control. The following paragraphs deal with the possible improvement of the circuit to VCO.

_{1}resistor in the topology (Figure 1) of the oscillator requires the implementation of controllable resistance in a floating form. The replacement of R

_{1}by the emulator based on active devices, for example, operational transconductance amplifiers (OTAs) [30,31], brings significant additional power consumption, area, and further complications. Therefore, we selected the optocoupler NSL-32SR3 [32] (photodiode-photoresistor) with very favorable features (frequency bandwidth and linearity) in a grounded or floating form in comparison with many active solutions (unipolar transistors in a linear regime). Our circuit (Figure 1) employs two optocouplers as shown in Figure 3.

_{m}

_{1,2}= 910 Ω and R

_{pot}= 2.5 kΩ result from the required transformation (R

_{m}

_{1,2}) of the driving voltage V

_{OC}to currents with a maximal allowed value (here approximately 1.5 mA per branch, which is approximately more than 10 times lower current consumption than opamp or CCII per single supply branch, for V

_{OC}= 5 V—fully positive supply voltage) and the compensation for the slight inequality of the resulting R

_{OC}

_{1}and R

_{OC}

_{2}(given by fabrication mismatch) for the same driving current. We compensated this effect by the slight inequality of driving currents (I

_{OC}

_{1}≠ I

_{OC}

_{2}). The threshold voltage V

_{th}≈ 1.6 V of the optocoupler’s LED was obtained experimentally. The measured frequency features (by vector network analyzer E5071C) of the optocoupler output (Z

_{OC}) are introduced in Figure 4 for particular values. Figure 5 shows the dependence of R

_{OC}on the driving current and voltage (in accordance with the driving circuitry in Figure 3). The datasheet [32] does not publish these features, but they must be known for the design of applications. Features of the device limit its implementation to systems operating around 10 MHz when the value of R

_{OC}is set below 500 Ω. Based on our experiments, the relation between R

_{OC}and the driving current I

_{OC}can be found empirically as R

_{OC}[Ω] ≅ 0.2/I

_{OC}[A]. Then R

_{OC}can be approximately expressed, in dependence on the driving voltage V

_{OC}, as:

_{OC}

_{1}≠ I

_{OC}

_{2}, the ideal equation for the FO (f

_{0i}) controlled by the optocoupler can be written as:

_{1,2}; above 1 MHz) for the FO (f

_{0e}) can be obtained for real values of parasitic features included in Equation (5c). We expect identical values R

_{X1}= R

_{X2}= R

_{X}= 95 Ω (and C

_{p}

_{1}= 3 pF, C

_{p}

_{2}= 10 pF) in the following expression:

_{OC}adjustability, from approximately 130 Ω to 2.7 kΩ (I

_{OC}varied from 75 μA to 1500 μA) in the ideal case and from 150 Ω to 2.8 kΩ in the measured case, see Table 3 for the detailed results. The expected trace includes the abovementioned parasitic elements. These results are represented graphically in Figure 6a, and the FO dependences for the driving of the oscillator by V

_{OC}voltage are shown in Figure 6b. The traces in Figure 6b represent the ideal (Equation (7)), expected (Equation (8), including the nodal parasitics of the circuit), and the additional nodal capacitances (10 pF) expected in the case of the real printed circuit board. Finally, the measured results are very close to the case in which PCB parasitics are considered. The CO for the influenced circuit (as derived in Equation (5b)) is fulfilled theoretically for B ≥ 1.12.

_{OC}in Table 3 and Figure 6b): (a) parasitic elements (capacities) of the active element due to the close values of the working capacitors to the stray capacitances; (b) transit features of active devices (their phase responses are especially important for oscillators—these issues occur at frequencies lower than −3 dB cut-off or transit frequency); (c) Miller effect of the increasing input capacity of active devices (amplifiers) when the gain is varied—the “parasitic capacity” increases with increasing gain of blocks of the circuit; this behavior is not easily predictable and implementable to the design equations; (d) high uncertainties in bands above 1 MHz given by real parasitic features of the PCB (parasitic conductivity, inductance, and capacity) that can be only approximately estimated in the case of capacity—the accuracy and high-frequency (RF) behavior of circuits operating above 1 MHz highly depends on the design and quality of the PCB; and (e) inequality of the driving current of optocouplers (I

_{OC}

_{1}≠ I

_{OC}

_{2}).

_{1,2}and R

_{OC}

_{1,2}) supposes a range of the FO tunability of 1.04 MHz→25.27 MHz. Calculations including all important parasitic effects estimate a range of 0.89 MHz→13.32 MHz (R

_{1,2}varied from 247 to 2.88 kΩ). Consideration of the additional PCB effect (+10 pF) leads to a range of 0.75→11.21 MHz. The experimental values follow our expectations because the measured FO yields a range of 1.05→10.30 MHz.

_{C}

_{1}and V

_{C}

_{2}) reach levels of about 200 mV

_{p}

_{-p}and 300 mV

_{p}

_{-p}(based on the setting of the AGC) and they remain almost constant during the tuning process (Figure 7a). Their ratio confirms the validity of Equation (4). The phase shift of both signals is around 45 degrees (Figure 7b). This value was obtained from the oscilloscope in the time-domain measurement by the automatic function evaluating the distance at which signals at both channels cross 0. An example of transient responses for V

_{OC}= 4.95 V (f

_{0meas}= 10.30 MHz) is shown in Figure 8. Their spectral analysis provided the results shown in Figure 9. The THD varies between approximately 0.7 and 3.3%. Quite high values are given by the low suppression of higher harmonic components of the active device itself (especially by the high-speed device OPA615 [28], only about 35 dBc in MHz bands). Similarly, the implementation of many nonlinear high-speed devices results in a certain presence of somewhat influential intermodulation products (visible in transient responses as superposed fluctuations at peaks of amplitudes as well as some combination products observed in the spectral analysis around the fundamental tone). The overall power consumption of the testbed (including buffers and opamps in AGC) reaches 570 mW (five IC devices, approximately 60 mA of power current per supply branch, ±5 V).

_{1,2}= 4.7 pF was selected). Then, the value f

_{0}= 25 MHz was set experimentally by V

_{OC}= 4.55 V. The results of the spectral analysis are shown in Figure 10 for both output waveforms. Images of the measured prototype are given in Figure 11.

_{C}

_{2}output (these values are actually almost identical for both outputs). The phase noise value was obtained for offset frequency ∆f

_{offset}= 10 kHz and 100 kHz (1/1000 and 1/100 of fundamental tone; the oscillator frequency was set to f

_{0}≅ 10 MHz by V

_{OC}= 4.92 V for this test). The phase noise values of 45 and 47 dBc/Hz were obtained for these values of offset frequencies. Note that these are only approximate values due to the limited accuracy of measurement (the noise background is influenced by the resolution-bandwidth (RBW) of the spectrum analyzer that was set to 10 Hz in all cases). The value in the range of 40→70 dBc/Hz is typical for these types of circuits due to the usage of inertial AGC (it solves limitation, shape distortion, THD, and the variation of output levels when f

_{0}is tuned, but its drawback is the higher fluctuation/jitter of output amplitudes). Radio-frequency (GHz)-targeted solutions reach values in the high tens of dBc/Hz (for example >100 dBc/Hz) in dependence on ∆f

_{offset}because there is no AGC system in narrow-band tunable oscillators and higher spurious spectral products are filtered. However, this approach cannot be used in base-band or inter-frequency-band oscillators tunable in the f

_{0}range of 10:1 or more. Note that the phase noise and f

_{0}stability (except AGC) also depend on the precision of the construction of the circuit (quality of the PCB, etc.). It may significantly influence overall performances, especially at high frequencies above 1 MHz. The fundamental tone slightly fluctuates in the results shown in Figure 12. The frequency change achieves ±33 kHz (±0.33% at f

_{0}≅ 10 MHz), which results in a frequency stability of S(f

_{0}) = |∆f

_{0}/f

_{0}| = 6.6 × 10

^{−3}(being within the typical range for active RC oscillators).

## 6. Discussion of Other Methods of Indirect Electronic Control of FO

_{1}is not very beneficial due to the floating (between two nodes) connection to the circuit. The method discussed in the previous paragraphs implemented optocouplers; however, there are also other possibilities that should be briefly discussed (their main advantages and disadvantages). Table 4 reveals their general comparison.

_{1,2}by junction field effect transistors (J-FET) in a triode/ohmic/linear regime [11,12,33,34,35] can be easily applied. However, there are some restrictions. It is not easy to maintain a transistor in a linear regime (V

_{DS}< V

_{GS}− V

_{th}) even for increasing processed signal levels in nodes where transistors are connected. Transistors behave highly nonlinearly for voltage levels higher than several tens of mV, and nonlinearity increases for increased resistance (r

_{DSon}) driven by V

_{GS}voltage. The range of the r

_{DSon}resistance adjustability can be large (N type J-FET BF245A [36]: 200 Ω→2 kΩ for 0→−2 V); however, the nonlinearity of V

_{DS}vs. I

_{D}plots plays a significant role, especially for high values of resistances (high V

_{GS}). Unfortunately, there is no other way in the IC design practice. One example of J-FET implementation was experimentally tested in our oscillator (Figure 1). Figure 13 illustrates the output level for the V

_{C}

_{1}wave that is significantly distorted (THD > 13%) by nonlinearity with increased values of r

_{DSon}. The amplitude is not limited but the shape and symmetry of the positive half-wave vs. negative half-wave is significantly damaged. The linearization of the transistor can be provided by two additional resistors [33]; however, the linearization of the floating form of an electronically controllable equivalent is not an easy task (many additional active and passive devices are required) [34,35].

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Frequency responses of the optocoupler output stage impedance: (

**a**) magnitude plots; (

**b**) phase response plots.

**Figure 6.**Dependences of FO on: (

**a**) R

_{1,2}(formed by R

_{OC}

_{1,2}only or R

_{OC}

_{1,2}influenced by R

_{X}

_{1,2}= 95 Ω); (

**b**) V

_{OC}(traces obtained from ideal, expected, and measured results).

**Figure 7.**Effects of the FO tuning on the generated signals: (

**a**) dependence of output levels on the FO, (

**b**) dependence of phase shift on the FO.

**Figure 8.**Example of the produced output waveforms in time domain at the end of designed range of the FO adjustment.

**Figure 9.**Spectrum of generated waveforms at the end of designed range of the FO adjustment: (

**a**) V

_{C}

_{1}; (

**b**) V

_{C}

_{2}.

**Figure 10.**Spectrum of generated waveforms for C

_{1,2}= 4.7 pF and V

_{OC}= 4.55 V: (

**a**) V

_{C}

_{1}; (

**b**) V

_{C}

_{2}.

**Figure 12.**Spectral analysis for phase noise measurement at V

_{C}

_{2}: (

**a**) offset frequency 10 kHz; (

**b**) offset frequency 100 kHz.

**Figure 13.**The example of distorted waveform by nonlinear effects of junction field effect transistors (J-FET) replacing resistors.

**Table 1.**Comparison of solutions of the simplest resistance-controllable oscillators and single-resistance-controllable oscillator (SRCO) types based on two active elements with three-port current conveyors and grounded capacitors.

Reference (Year) | Number of Active/Passive Elements | Type of Active Element(s) | Number and Type of Elements Suitable for Frequency of Oscillation (FO) Control | Allowed Character of FO Dependence | Tested Character of FO Dependence | Maximal Value of Tested FO (MHz) | Total Harmonic Distortion (THD) (%) | Power Consumption (mW) | Phase Noise (dBc/Hz) | Number and Type of Elements Suitable for Condition of Oscillation (CO) Control | Active Parameter for CO Control | Generated Levels (Amplitudes) Independent of Tuning Process | Produced Phase Shift (Degrees) | Verification | Amplitude Stabilization |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

[3] (1995) | 2/5 | CCI+, CCII− | 1 R grounded | ~R^{−1/2} | ~R^{−1/2} | 0.042 | N/A | N/A | N/A | 1 R grounded | - | N/A | N/A | M | N/A |

[4] (1996) | 2/5 | CCI−, CCI− | 1 R grounded | ~R^{−1/2} | N/A | N/A | N/A | N/A | N/A | 1 R grounded | - | N/A | N/A | S | Yes ^{a} |

[5] (1996) | 2/5 | CFOA | 1 R grounded | ~R^{−1/2} | ~R^{−1/2} | 0.460 (9.85) ^{I} | N/A | N/A | N/A | 1 R grounded | - | N/A | N/A | M | N/A |

[6] (1997) | 2/5 | CFOA | 1 R grounded | ~R^{−1/2} | ~R^{−1/2} | 6.00 | <1 | N/A | N/A | 1 R grounded | - | N/A | N/A | M | N/A |

[7] (1998) | 2/5 | CFOA | 1 R grounded | ~R^{−1/2} | ~R^{−1/2} | N/A | N/A | N/A | N/A | 1 R grounded | - | N/A | N/A | N/A | N/A |

[8] (1998) | 2/5 | CFOA | 1 R grounded | ~ R^{−1/2} | N/A | 0.260 | N/A | N/A | N/A | 1 R grounded | - | N/A | N/A | M | N/A |

[9] (1999) | 2/6 (5) | CCII+, CCII− | 2 R grounded | ~R^{−1} | N/A | 0.153 | N/A | N/A | N/A | 2 R grounded | - | N/A | 90 | S | N/A |

[10] (2005) | 2/6 | CCII+ (CFOA) | 1 R grounded | ^{b} | ^{b} | 0.189 | 1.5 | N/A | N/A | 1 R floating | - | N/A | N/A | S | N/A |

[11] (2006) | 2/5 | CFOA | 1 R floating or grounded ^{c} | ~R^{−1/2} | ~R^{−1/2} | 0.037 | <3.1 | N/A | N/A | ^{c} | - | N/A | N/A | M | N/A |

[12] (2009) | 2/5 | CFOA | 1 R grounded | ~R^{−1/2} | ~R^{−1/2} | 290 (609) ^{II} | 1.6 | N/A | N/A | 1 R grounded | - | N/A | N/A | M | N/A |

[13] (2010) | 2/4 | CFOA | ^{d} | ~R^{−1/2} | N/A | N/A | N/A | N/A | N/A | ^{d} | - | N/A | N/A | M | N/A |

[14] (2010) | 2/2 | CCCII+/- | 2 R_{X} | ~R^{−1} | ~R^{−1/2} | 1.80 | <7 | 3.5 | N/A | - | B | N/A | N/A | S | N/A |

[15] (2011) | 2/5 | CFOA | 1 R grounded | ~R^{−1/2} | N/A | 1.320 | <3 | N/A | N/A | 1 R floating | - | N/A | N/A | M | N/A |

[16] (2011) | 2/4 | CFOA | 1 C_{eq} grounded | ~C_{eq}^{−1/2} | N/A | 0.146 | <2 | N/A | N/A | 2 R floating * | - | N/A | 90 | S | N/A |

[17] (2012) | 2/4 | DO-(I)CCII, CCI | 2 R floating and grounded | ~R^{−1} | ~R^{−1/2} | 0.182 | <1.7 | N/A | N/A | ^{e}* | - | No | 90 | S | N/A |

[18] (2014) | 2/4 | CFOA | 2 R floating | ~R^{−1} | N/A | 0.065 (1.33) ^{III} | <0.8 | 0.86 | N/A | * | - | Yes | 90 | B | N/A |

[19] (2011) | 2/6 | CCII+ | 2 R floating and grounded | ~R^{−1} | N/A | 1.43 | <0.3 | N/A | N/A | ** | - | N/A | N/A | M | Yes |

Figure 1 | 2/4 | CCII−, ECCII+ | 2 R floating and grounded | ~R^{−1} | ~R^{−1} | 10.3 (25.0) ^{IV} | <3.3 | 570 ^{V} | >45 | - | B | Yes | 45 | M | Yes |

_{X}—internal resistance of terminal X (current conveyor); B—adjustable current gain between X and Z terminal of ECCII.

^{a}Antiparallel diodes;

^{b}complicated matching condition (resistor ratio) for tuning;

^{c}several various solutions presented in Reference [11], not all of them have easily uncoupled CO and FO;

^{d}complex relations for FO and CO, some of them have uncoupled FO and CO independently controllable by grounded resistors;

^{e}sometimes uncomfortable condition for CO (equality/matching of two capacitors/resistors required, no further parameter available for driving of CO), independence of generated levels (amplitudes) on FO confirmed analytically; * problematic FO tuning and CO adjusting by matching of two resistors (R

_{1}= R

_{2}or C

_{1}= C

_{2}for CO driving and R

_{1}R

_{2}for FO tuning); ** matching of two resistors intended for FO must be ensured for uncoupled CO control by different pair of resistors;

^{I}up to 9.85 MHz without working capacitors (used with parasitic nodal capacitances only);

^{II}609 kHz available for 0.5 nF values of capacitors;

^{III}measured at 65 kHz with commercial element, simulated with CMOS topology of active device at 1.33 MHz;

^{IV}high corner of tunability range set to 10.3 MHz but 25 MHz available when external C

_{1,2}= 4.7 pF applied,

^{V}this value includes power consumption of all devices on experimental printed circuit board (PCB) (also voltage buffers, automatic gain control circuit for amplitude stabilization (AGC), etc.); M—measured; S—simulated, B—both; N/A—not available, not tested.

Reference | [14] | [17] (Figure 1a) | Proposed (Figure 1) |
---|---|---|---|

No. of passive elements | 2 | 4 | 4 |

No. of elements (parameters) suitable for FO control | 2 | 2 | 2 |

No. of elements (parameters) used for FO control | 1 | 1 | 2 |

Solution of FO control | resistance (R_{X}) of X terminal | external resistance value (in X terminal of conveyor) * | resistances of optocouplers |

Allowed character of FO dependence | ~R^{−1} | ~R^{−1} | ~R^{−1} |

Tested character of FO dependence | ~R^{−1/2} | ~R^{−1/2} | ~R^{−1} |

Range of driving force | 1 μA→500 μA | 8 kΩ→15 kΩ * | 1.73→4.95 V |

Ratio of driving force | 500:1 (bias current) | 1.9:1 * | 3:1 (control voltage) |

Obtained FO range (MHz) | 0.2→1.8 | 0.120→0.165 | 1.05→10.30 |

Ratio of FO | 9:1 | 1.4:1 | 10:1 |

Active parameter for CO control | Yes | No | Yes |

Type of active parameter suitable for CO control | current gain | N/A | current gain |

Outputs (nodes) used | 1 | 2 | 2 |

Produced phase shift (°) | N/A | 90 | 45 |

Amplitude stabilization | N/A | N/A | Yes |

Generated levels (amplitudes) independent on tuning process | N/A | No | Yes |

Output amplitude | 25 mV | 80→125 μA, 95→110 μA | 100 mV, 150 mV |

THD (%) | 1→7 | 0.7→1.4 | 0.7→3.3 |

Verification | simulated | simulated | measured |

**Table 3.**Comparison of ideal, expected, and measured (experimental) FO dependences on driving parameters.

V_{OC} (V) | I_{OC} (μA) | R_{OCi} (Ω) | R_{OCmeas} (Ω) | R_{OCi} + R_{X1,2} (Ω) | R_{OCmeas} + R_{X1,2} (Ω) | f_{0i} (MHz) | f_{0e} (MHz) | f_{0e + 10pF} (MHz) | f_{0meas} (MHz) |
---|---|---|---|---|---|---|---|---|---|

4.95 | 1500 | 133 | 152 | 228 | 247 | 25.27 | 13.32 | 11.21 | 10.30 |

3.74 | 884 | 226 | 227 | 321 | 322 | 16.78 | 10.05 | 8.46 | 8.01 |

2.82 | 500 | 400 | 366 | 495 | 461 | 9.57 | 6.64 | 5.59 | 6.02 |

2.23 | 280 | 714 | 629 | 809 | 724 | 5.18 | 3.98 | 3.35 | 4.00 |

2.04 | 193 | 1039 | 936 | 1134 | 1030 | 3.45 | 2.77 | 2.33 | 3.01 |

1.86 | 123 | 1633 | 1524 | 1727 | 1620 | 2.04 | 1.70 | 1.43 | 2.01 |

1.73 | 75 | 2667 | 2780 | 2762 | 2880 | 1.04 | 0.89 | 0.75 | 1.05 |

_{1,2}.

**Table 4.**Comparison of the methods for indirect FO tunability (standard potentiometer shown for reference purposes).

Method | Frequency Features | Dynamical Features | Linearity | Response on Control | Value Range | Significant Additional Power Consumption | Notes |
---|---|---|---|---|---|---|---|

Resistor (potentiometer) | good * | good | good | fast | large (several decades) | No | mechanical features |

Optocoupler with resistive output | good * | good (hundreds of mV) | good (nonlinear deviation up to units of %) | average (units of ms) | large | No | - |

J-FET (or unipolar transistor) | good | bad (tens of mV) | bad (nonlinear deviation tens of %) | fast | large | No | maintain in linear regime |

Digital potentiometer | ** | good | good | ** | limited (number of switched segments/bits) | Yes | discontinuous adjusting |

D/A converter | *** | good | good | *** | limited (number of bits) | Yes | discontinuous adjusting |

Active analog solution (OTA for example) | good | average/bad | average/bad | fast | limited (can be even less than a decade for MOS solution) | Yes | - |

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**MDPI and ACS Style**

Sotner, R.; Jerabek, J.; Langhammer, L.; Dvorak, J.
Design and Analysis of CCII-Based Oscillator with Amplitude Stabilization Employing Optocouplers for Linear Voltage Control of the Output Frequency. *Electronics* **2018**, *7*, 157.
https://doi.org/10.3390/electronics7090157

**AMA Style**

Sotner R, Jerabek J, Langhammer L, Dvorak J.
Design and Analysis of CCII-Based Oscillator with Amplitude Stabilization Employing Optocouplers for Linear Voltage Control of the Output Frequency. *Electronics*. 2018; 7(9):157.
https://doi.org/10.3390/electronics7090157

**Chicago/Turabian Style**

Sotner, Roman, Jan Jerabek, Lukas Langhammer, and Jan Dvorak.
2018. "Design and Analysis of CCII-Based Oscillator with Amplitude Stabilization Employing Optocouplers for Linear Voltage Control of the Output Frequency" *Electronics* 7, no. 9: 157.
https://doi.org/10.3390/electronics7090157