CN109308388A - Electric current fractional order integration control formula recalls sensor - Google Patents
Electric current fractional order integration control formula recalls sensor Download PDFInfo
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- CN109308388A CN109308388A CN201811060046.7A CN201811060046A CN109308388A CN 109308388 A CN109308388 A CN 109308388A CN 201811060046 A CN201811060046 A CN 201811060046A CN 109308388 A CN109308388 A CN 109308388A
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- G06F30/36—Circuit design at the analogue level
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Abstract
The invention discloses a kind of electric current fractional order integration control formulas to recall sensor, including pin a, pin b, voltage-controlled inductor UL, inductor L, current-controlled voltage source IUWith voltage fractional order integrator A, voltage-controlled inductor ULIncluding voltage controling end ucWith controlled inductance Lu, controlled inductance LuInductance by voltage controling end ucVoltage value control, current-controlled voltage source IUIncluding current controling end i and controlled voltage source output terminal ui, controlled voltage source output terminal uiVoltage value controlled by the current value of current controling end i, voltage fractional order integrator A includes voltage input end uiIt is u with voltage output endc.Sensor M is recalled in the equivalent lotus control of electrical characteristic that electric current fractional order integration control formula recalls sensor pin a, bLA, B pin characteristic, be two pins, have the advantages that recall inductance value variation range it is flexible, it is no ground limit, operating voltage range is wide and should be readily appreciated that.
Description
Technical field
The invention patent relates to novel circuit design fields, and in particular to a kind of electric current fractional order integration control formula recalls sense
Device.
Background technique
Divide anti-(fractance), is the abbreviation of fractional order impedance (fractional-order impedance), is to have
The electronic component or system of fractional calculus (fractional-order calculus) calculation function.Circuit, which is realized, to be divided
The number required primary element of rank calculus operation is referred to as a point anti-member (fractor).Preferably dividing anti-member is to be not present
, approximate realization circuit, which is known as dividing resisting, accordingly approaches circuit.Point anti-, point anti-member, it is point anti-approach circuit be fractional order circuit with
The key components of system, fractional order circuit and system are an emerging interdisciplinary research fields.
2001, a point anti-member was replaced classical Wien bridge oscillator (Wien-bridge by W.Ahmad et al.
Oscillator the capacitor in) obtains fractional order Wien bridge oscillator.2008, A.G.Radwan and A.S.Elwakil et al.
The circuit of the working principle and a variety of fractional order oscillators that provide fractional order oscillator realizes case.Due to true inductor and electricity
Container is with fractional order computation performance, and 2013, Wang Fa-Qiang et al. combined fractional calculus, studies open loop
The continuous conduction mode characteristic of Buck converter transfer function, and carry out the PSIM simulation analysis of circuit.2011,
The series circuit that A.G.Radwan et al. careful analysis is made of the anti-member of capacitive point and the anti-member of perception point, and provide numerical value calculating
With Simulation results.2014, Diao Lijie, old Supreme Being she et al. systematically analyze and summarize by resistance, capacitive point anti-member and sense
Property point anti-member fractional order circuit in parallel constituted essential characteristic and rule, analyze pure void specific to circuit under the conditions of fractional order
Impedance problems.2016, A.E.Calik et al. analyzed the change of the anti-member of capacitive point and the anti-first series circuit charge of perception point at any time
Law.Dividing anti-member is also the key element that fractional order Hopfield nerve network circuit is realized, fractional order Hopfield nerve
Network application has obtained excellent performance in anti-chip clone field.In short, anti-by dividing for fractional calculus operation is able to achieve
Member, which is applied to classical circuit and obtains fractional order circuit, has become one of research hotspot of Circuits and Systems, fractional order circuit and system
Its unique advantage is gradually manifested.
1971, the Cai Shaotang of University of California Berkeley was taught from Circuit theory completeness, predicted characterization
The passive basic circuit elements of relationship between charge and magnetic flux, and it is named as memristor (memristor).Favour in 2008
Physics realization memristor is announced in general laboratory, is caused the extensive concern of academia and industry, is started people and grind to memristor
The upsurge studied carefully.Memristor is the 4th kind of generally acknowledged basic circuit elements.2009, recalls container (memcapacitor) and recall sensor
(meminductor) new concept is also suggested.With memristor and recall as container, the indicatrix for recalling sensor is also to pinch hysteresis
Line recalls the indicatrix of sensor the difference is that recall sensor foundation is the State-dependence relationship between magnetic flux and current value
It is that hysteresis curves are pinched in Wei An domain.
With going deep into for correlative study, realize that the memristor circuit with fractional calculus operational performance starts to be ground
The concern for the person of studying carefully becomes one of fractional order circuit and systematic research forward position.2010, IvoFractional order is obtained for the first time
Memristor cai's circuit, the numerical solution circuit equation, and the dynamic behavior and stability of circuit are analyzed, this is disclosed document
In report circuit simultaneously containing point anti-member and memristor for the first time.2015, Yu Yajuan et al. was based on the linear memristor of HP TiO2
Doped layer thickness cannot be equal to the fact that zero or device integral thickness, propose the linear memristor of fractional order HP TiO2, grind
When by period external excitation operation rank is studied carefully to the affecting laws of its memristor value dynamic range and output voltage dynamic amplitudes, but not
Provide the linear memristor circuit of fractional order HP TiO2 or device designs.2016, PuYi-Fei et al. was proposed and is analyzed point
The concept and theory for recalling anti-member are given at the position in Cai Shi periodic table, and attempted to divide trellis scale in anti-in 2017
Resistance is substituted by memristor equivalent circuit, and analog circuit realization point is recalled anti-.2017, Gangquan Si et al. was in providing a kind of point
Number rank Charge controlled memristor, the fractional order integration operation containing electric current, Gangquan Si et al. have carried out theory analysis sum number
It is worth emulation experiment.2017, SomiaH.Rashad et al. resists using point approached first device such as circuit, current transmission device and multiplier
Part, circuit realize a kind of electric current fractional order integration control formula memristor, are a kind of extraordinary trials.But SomiaH.Rashad
Et al. electric current fractional order integration control formula memristor, need one end to be grounded, the voltage range of input signal is by internal current
The supply voltage of transmitter limits.
It is real to have no that electric current fractional order integration control formula recalls sensor design, principle analysis and circuit at present for comprehensive literature discovery
Existing etc. research report.Electric current fractional order integration control formula recalls sensor, the operation rank index of fractional order product device is introduced, than electricity
It is more flexible that stream integration control formula recalls sensor, and current integration control formula recalls sensor and can regard electric current fractional order integration control formula as and recalls sense
Device operation rank extends to 1 special case.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of electric current fractional order integration control formulas to recall sensor, solves existing
Current integration control formula recalls the problem of sensor can not achieve the control of electric current fractional order integration.
The technical scheme to solve the above technical problems is that a kind of electric current fractional order integration control formula recalls sensor,
Including pin a, pin b, voltage-controlled inductor UL, inductor L, current-controlled voltage source IUIt is described with voltage fractional order integrator A
Voltage-controlled inductor ULIncluding voltage controling end ucWith controlled inductance Lu, the voltage-controlled inductor ULInterior controlled inductance LuInductance by
Voltage controling end ucVoltage value control, the current-controlled voltage source IUIncluding current controling end i and controlled voltage source output terminal
ui, the current-controlled voltage source IUInterior voltage output terminal uiVoltage value controlled by the current value of current controling end i, it is described
Voltage fractional order integrator A includes voltage input end uiIt is u with voltage output endc, the pin a, voltage-controlled inductor ULIt is controlled
Inductance Lu, inductor L, current-controlled voltage source IUCurrent controling end and pin b be series relationship, current control electricity
Potential source IUInterior controlled voltage source output terminal is connected with voltage input end in voltage fractional order integrator A, the voltage fractional order product
Divide voltage output end and voltage-controlled inductor U in device ALInterior voltage controling end is connected；From the moment 0 to moment t, the voltage fractional order
The voltage value of voltage output end in integrator AKiFor the proportionality coefficient of voltage fractional order integrator A,
- 1 < μ < 0 of operation rank,For integral operation symbol, the moment 0 is the lower limit of fractional order integration, and moment t is fractional order integration
The upper limit.
Based on the above technical solution, the present invention can also be improved as follows.
Further, the voltage-controlled inductor ULInterior controlled inductance LuInductance Lu=Kl×uc, KlFor voltage-controlled inductor UL
Control coefrficient.
Further, the current-controlled voltage source IUThe output voltage u of interior voltage output endi=Kj× i, KjFor electric current control
Voltage source I processedUControl coefrficient.
The beneficial effects of the present invention are: in the present invention, electric current fractional order integration control formula recalls the electricity of sensor pin a, b
The equivalent characteristic for recalling sensor of gas characteristic, is two pins, has and recalls flexible inductance value variation range, no ground limitation, operating voltage
The advantages of range is wide and should be readily appreciated that.
Detailed description of the invention
Fig. 1 is the principle of the present invention figure
Sinusoidal current source i (t) current value and magnetic flux when Fig. 2 is operation rank μ=- 0.4 in the embodiment of the present inventionReason
By graph of relation
Sinusoidal current source i (t) current value and magnetic flux when Fig. 3 is operation rank μ=- 0.6 in the embodiment of the present inventionReason
By graph of relation
String current source i (t) current value and magnetic flux when Fig. 4 is operation rank μ=- 0.8 in the embodiment of the present inventionTheory
Graph of relation
Fig. 5 is the amplitude-frequency characteristic curve graph in the embodiment of the present invention
Fig. 6 is the phase frequency characteristic curve diagram in the embodiment of the present invention
Fig. 7 is the rank frequency characteristic curve diagram in the embodiment of the present invention
Fig. 8 is the F characteristic curve diagram in the embodiment of the present invention
Fig. 9 is the amplitude-frequency characteristic simulation curve figure in the embodiment of the present invention
Figure 10 is the phase frequency characteristics simulation curve graph in the embodiment of the present invention
Figure 11 is the Multisim Software Simulation Test circuit diagram in the embodiment of the present invention
Sinusoidal current source i (t) current value and magnetic flux when Figure 12 is operation rank μ=- 0.4 in the embodiment of the present invention's
Simulation curve figure (frequency f=3Hz)
Sinusoidal current source i (t) current value and magnetic flux when Figure 13 is operation rank μ=- 0.4 in the embodiment of the present invention's
Simulation curve figure (frequency f=30Hz)
String current source i (t) current value and magnetic flux when Figure 14 is operation rank μ=- 0.4 in the embodiment of the present inventionIt is imitative
True curve graph (frequency f=300Hz)
Specific embodiment
The principle and features of the present invention will be described below with reference to the accompanying drawings, and the given examples are served only to explain the present invention, and
It is non-to be used to limit the scope of the invention.
As shown in Figure 1, a kind of extremely simple electric current fractional order integration control formula recalls sensor, including pin a, pin b, voltage-controlled electricity
Sensor UL, inductor L, current-controlled voltage source IUWith voltage fractional order integrator A, voltage-controlled inductor ULIncluding voltage controling end
ucWith controlled inductance Lu, voltage-controlled inductor ULInterior controlled inductance LuInductance by voltage controling end ucVoltage value control, electric current
Control voltage source IUIncluding current controling end i and controlled voltage source output terminal ui, current-controlled voltage source IUInterior voltage output terminal
uiVoltage value controlled by the current value of current controling end i, voltage fractional order integrator A includes voltage input end uiIt is defeated with voltage
Outlet is uc, pin a, voltage-controlled inductor ULControlled inductance Lu, inductor L, current-controlled voltage source IUCurrent controling end with
And pin b is series relationship, current-controlled voltage source IUInterior controlled voltage source output terminal and voltage in voltage fractional order integrator A
Input terminal is connected, voltage output end and voltage-controlled inductor U in voltage fractional order integrator ALInterior voltage controling end is connected；From the moment
The voltage value of voltage output end in 0 to moment t, the voltage fractional order integrator AKiFor voltage point
The proportionality coefficient of number rank integrator A, -1 < μ < 0 of operation rank,For integral operation symbol, the moment 0 is under fractional order integration
Limit, moment t are the upper limit of fractional order integration.
In embodiments of the present invention, voltage-controlled inductor ULInterior controlled inductance LuInductance Lu=Kl×uc, KlFor voltage-controlled electricity
Sensor ULControl coefrficient.
In embodiments of the present invention, current-controlled voltage source IUThe output voltage u of interior voltage output endi=Kj× i, KjFor
Current-controlled voltage source IUControl coefrficient.
The operation principle of the present invention is that:
Common fractional calculus definition has Riemann-Liouville (Riemann-Liouville) definition, Kapp figure
(Caputo) definition and Green Wa Er-Lai Te Nico husband (Gr ü nwald-Letikov) definition etc..From the moment 0 to moment t,- μ rank Riemann-Liouville fractional order of referred to as function f (t)
Integral, whereinFor integral operation symbol,For gamma function, the moment 0 is under fractional order integration
Limit, moment t are the upper limit of fractional order integration.When the initial value of function f (t) and its all-order derivative are 0, if f (t)=sin (ω0T), then haveIf f (t)=cos (ω0T), then haveω0For signal angular frequency.
If the initial value of function f (t) and its all-order derivative is 0, the Laplace transform of fractional calculus is
In formula, s is Laplace variable, also known as operation variable.
Voltage transfer function of the fractional order integrator A that the present invention uses in Laplace transform domain(- 1 < μ < 0).The fractional value μ given for one, the voltage transfer function of fractional order integrator A
H (s) is irrational function.Purchase at present is directly realized by the calculation function of transfer function H (s) less than commercial electronic component, and
The element and function that also not can be used directly inside Multisim circuit simulating software, Matlab computational science software etc. are real
The calculation function of existing H (s).In general, completing reality by circuit realization (divide to resist and approach circuit) or software construction operation module
Coefficient rational function Hk(s) calculation function, for approaching unreasonable fractional order transfer function under certain frequency, certain precision
H (s):
In formula, non-negative integer variable k ∈ N expression approaches a grade number, positive integer parameter nkAnd dkIt is multinomial to respectively indicate molecule
Formula Nk(s) and denominator polynomials Dk(s) number.
Rational function Hk(s) common implementation has the Carlson rational approximations using Regular Newton iterative method, zero pole
The Charef rational approximations, right of the Oustaloup rational approximations of the progressive fitting of distribution method of point, fractional power pole and Zero pole distribution
The Matsuda rational approximations etc. of number spacing frequency point continued-fraction expansion method.The embodiment of the present invention is forced using Oustaloup is reasonable
Closely.
The canonical form of Oustaloup rational approximations isIn formula, N is the grade approached
Number, zero pointPoleGainProportional coefficient KiBy
User is set as needed.Specific algorithm are as follows: (1) input fractional arithmetic rank μ, selection approaches frequency band ωb(low frequency point)
And ωh(high-frequency point), setting ratio COEFFICIENT KiWith approach a grade times N；(2) ω is calculatedu, then calculated by vector point processing
ω outk、ω'kAnd K；(3) the canonical form structure of the numerical value and Oustaloup rational approximations obtained according to (1) step and (2) step
Produce Oustaloup rational approximations functionOHk(s)。
Intuitively to analyze Oustaloup rational approximations function in frequency domain imageOHk(s) voltage transfer function H (s) is approached
Performance.Laplace variable s=j ω is taken, frequency index variable is enabledBy Oustaloup
Rational approximations functionOHk(s) amplitude-frequency characteristicPhase frequency featureRank frequency featureWith F featureCurve respectively with the amplitude-frequency characteristic of voltage transfer function H (s)Phase frequency feature
Rank frequency featureWith F featureCurve comparison.Width
Frequency characteristic function and phase frequency characteristic function feature fractional order integrator A to the amplifying power of input voltage signal in frequency domain respectively
And phase effect, rank frequency characteristic function feature fractional arithmetic rank μ, the F characteristic function of fractional order integrator A in frequency domain in frequency domain
Feature fractional order integrator A Proportional coefficient Ki。
If a, b both end voltage u (t) and port current i (t) that electric current fractional order integration control formula recalls sensor, which are used, is associated with ginseng
Direction is examined, then the relationship for describing its port current value and storing between magnetic flux isL (q) is electric current score
What rank integration control formula recalled sensor recalls inductance value.Recall inductance value L (q)=Lu(q) score of electric current i (t) during+L, q are time [0, t]
Rank integrated value, andμ indicates fractional arithmetic rank, Lu(q)=Kl×Ki×Kj×q(t)。
The mathematical relationship that electric current fractional order integration control formula recalls sensor is represented by
L (q)=L+Kl×Ki×Kj× q (t),
It follows that electric current fractional order integration control formula recalls the fractional order of sensor recalled inductance value L (q) and depend on electric current i (t)
Integrated value q (t), q (t) are internal state variable.Electric current fractional order integration control formula is recalled into two end of sensor connection sinusoidal current source i
(t) pumping signal, and i (t)=I are used asm× sin (2 π ft), ImFor the current peak of current source, f is the frequency of current source, angle
Frequencies omega=2 π f.State variableElectric current fractional order integration
The inductance value of recalling that control formula recalls sensor changes at any time, andElectric current point can be obtained
Number rank integration control formula recalls the magnetic flux of sensor
Obtaining current fractional order integration control formula recalls inductance L=2H, voltage-controlled inductance control coefrficient K in sensorl=0.5H/V,
Current-controlled voltage source control coefrficient Kj=100 Ω and voltage fractional order integrator Proportional coefficient Ki=10.Take excitation sinusoidal current
The peak I of source i (t)m=100mA, and state variable q (t) is 0 when t=0.The operation rank μ of voltage fractional order integrator A=-
When 0.4, electric current fractional order integration control formula is recalled when sinusoidal current source i (t) frequency f is respectively 3Hz, 30Hz, 300Hz and 3000Hz
Excitation sinusoidal current source i (t) current value and magnetic flux of sensorTheory analysis curve it is as shown in Figure 2.Voltage fractional order
When the operation rank μ=- 0.6 of integrator A, electric current fractional order when sinusoidal current source i (t) frequency f is respectively 1Hz, 20Hz and 200Hz
Integration control formula recalls excitation sinusoidal current source i (t) current value and magnetic flux of sensorTheory analysis curve such as Fig. 3 institute
Show.When the operation rank μ=- 0.8 of voltage fractional order integrator A, sinusoidal current source i (t) frequency f is respectively 1Hz, 5Hz and 100Hz
When electric current fractional order integration control formula recall excitation sinusoidal current source i (t) current value and magnetic flux of sensorTheory analysis
Curve is as shown in Figure 4.
The calculation function that the voltage transfer function H (s) of fractional order integrator A is realized for circuit simulation, takes Oustaloup to have
Manage the low frequency point ω approachedb=0.1rad/s, high-frequency point ωh=1500rad/s, fractional arithmetic rank μ=- 0.4, ratio system
Number Ki=1, a grade number N=6 is approached.Thus according to Oustaloup rational approximations specific algorithm, zero pole point form is obtained
Oustaloup rational approximations function
Oustaloup rational approximations functionOH6(s) and the amplitude-frequency characteristic curve of voltage transfer function H (s) as shown in figure 5,
Phase frequency indicatrix as shown in fig. 6, rank frequency indicatrix as shown in fig. 7, F indicatrix is as shown in Figure 8.Fig. 5, Fig. 6, Fig. 7 and
Ideal curve shown in Fig. 8 indicates that voltage transfer function H (s) corresponding curve, approximating curve indicate Oustaloup rational approximations
FunctionOH6(s) corresponding curve.By curve graph 5, Fig. 6, Fig. 7 and Fig. 8 it can be seen that in low frequency point ωb, high-frequency point ωh
Approximate error is larger, but can be to avoid using this frequency band, Oustaloup rational approximations functionOH6(s) reached and approached effect
Fruit.The amplitude-frequency that Pspice is analyzed is carried out using the transactional analysis function (ACAnalysis) of Multisim circuit simulating software
Characteristics simulation curve is as shown in figure 9, phase frequency characteristics simulation curve is as shown in Figure 10.The rank frequency characteristics simulation obtained by emulation data
Shown in simulation curve of the F indicatrix that curve is obtained as shown in the simulation curve in Fig. 7, as emulation data such as in Fig. 8.Emulation
Analysis result is consistent with theory analysis, it was demonstrated that can use Oustaloup rational approximations functionOH6(s) it is passed to complete fractional order voltage
The calculation function of defeated function H (s).
Electric current fractional order integration control formula memristor is built in Multisim circuit simulating software according to structure shown in Fig. 1
The voltage transfer function H (s) of analogue system, fractional order integrator A uses the Oustaloup rational approximations function having verified thatOH6
(s).The Multisim Software Simulation Test circuit that electric current fractional order integration control formula recalls sensor is as shown in figure 11, and XCP2 is electric current
Probe, XSC2 are oscillographs.The excitation sinusoidal current that formula recalls sensor is controlled to obtain electric current fractional order integration in simulation software
Source i (t) current value and two pin magnetic fluxRelation curve, need to be by magnetic fluxIt is converted into the equal voltage of numerical value therewith
Value, so as to oscillograph observation.As shown in figure 11, two pin of sinusoidal current source is connected to voltage fractional order integrator A2Input,
Voltage fractional order integrator A2Output uo(t) it is connected to the channel A of oscillograph.From moment t0To tn, voltage integrator A2It is defeated
Voltage outui(t) formula is controlled for electric current fractional order integration recall sensor port voltage, setting voltage point
Number rank integrator A2Proportional coefficient KI=1.Voltage fractional order integrator A2Output voltage and magnetic control recall condenser circuit emulation magnetic
FluxRelationship are as follows:Realize voltage fractional order integrator A2Output voltage values table
Show that magnetic control recalls condenser circuit emulation magnetic flux, realizes observation of the oscillograph to magnetic flux.
Parameter selected when Voltammetric Relation theoretical curve according to Fig.2, obtaining sinusoidal current source i (t) frequency f is
Current source i (t) current value and magnetic flux when 3HzBetween simulation curve it is as shown in figure 12, sinusoidal current source i (t) frequency
Current source i (t) current value and magnetic flux when rate f is 30HzBetween simulation curve it is as shown in figure 13, sinusoidal current source i
(t) current source i (t) current value and magnetic flux when frequency f is 300HzBetween simulation curve it is as shown in figure 14, emulation
As a result consistent with theoretical curve as shown in Figure 2.
The above shows that electric current fractional order integration control formula recalls sensor a and b pin Wei An theory analysis curve and emulation
As a result identical, and meet and recall sensor MLThree substantive characteristics: 1. sinusoidal current source i (t) motivate lower electric current fractional order integration
The Wei An characteristic curve that control formula recalls sensor is to pinch hysteresis curves；2. pinching hysteresis curves lobe area to increase with sinusoidal current source frequency f
Reduce；3. sinusoidal current source frequency f tends to pinch hysteresis curves when infinity and is punctured into straight line.Prove the present invention and embodiment
It is feasible.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (3)
1. a kind of fractional order integration control formula recalls sensor, including pin a, pin b, voltage-controlled inductor UL, inductor L, current control
Voltage source IU, which is characterized in that including voltage fractional order integrator A, the voltage-controlled inductor ULIncluding voltage controling end ucWith by
Control inductance Lu, the voltage-controlled inductor ULInterior controlled inductance LuInductance by voltage controling end ucVoltage value control, the electricity
Current-controlled voltage source IUIncluding current controling end i and controlled voltage source output terminal ui, the current-controlled voltage source IUInterior controlled electricity
Potential source output end uiVoltage value controlled by the current value of current controling end i, the voltage fractional order integrator A includes that voltage is defeated
Enter to hold uiIt is u with voltage output endc, the pin a, voltage-controlled inductor ULControlled inductance Lu, inductor L, current controlled voltage
Source IUCurrent controling end and pin b be series relationship, the current-controlled voltage source IUInterior controlled voltage source output terminal and electricity
Voltage input end in fractional order integrator A is pressed to be connected, voltage output end and voltage-controlled inductor in the voltage fractional order integrator A
ULInterior voltage controling end is connected；From the moment 0 to moment t, the voltage value of voltage output end in the voltage fractional order integrator AKiFor the proportionality coefficient of voltage fractional order integrator A, -1 < μ < 0 of operation rank,For integral operation
Symbol, moment 0 are the lower limit of fractional order integration, and moment t is the upper limit of fractional order integration.
2. voltage-controlled inductor U according to claim 1L, which is characterized in that the voltage-controlled inductor ULInterior controlled inductance Lu
Inductance Lu=Kl×uc, KlFor voltage-controlled inductor ULControl coefrficient.
3. current-controlled voltage source I according to claim 1U, which is characterized in that the current-controlled voltage source IUInterior electricity
Press the output voltage u of output endi=Kj× i, KjFor current-controlled voltage source IUControl coefrficient.
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