CN105959000A - Memristor-based rapid start-up crystal oscillator - Google Patents

Abstract

The invention discloses a memristor-based rapid start-up crystal oscillator comprising a crystal resonator, a temperature compensation network, and an oscillation circuit module. The oscillation circuit module comprises MOS or BJT active devices, inductor and resistor passive devices, and a memristor network formed by m*n memristors. In virtue of the continuously variable resistance values of the memristors, the equivalent negative resistance of the oscillation circuit module is increased by regulating the resistance values of the memristors. Thus, the start-up time of the crystal oscillator is shortened and the difficulty in crystal oscillator circuit design is reduced.

Description

A kind of fast start-up crystal oscillator based on memristor

Technical field

The invention belongs to integrated circuit fields, relate to crystal oscillating circuit, be specially a kind of based on memristor, can fast start-up Crystal oscillator.

Background technology

Crystal oscillator, as stable frequency reference source, is widely used in FREQUENCY CONTROL and the field such as management, real frequency meter amount.Property Crystal oscillator that can be good requires low in energy consumption, and phase noise is little, and frequency stability is high, and Induction Peried is little.

Fig. 1 (a) is the structured flowchart of the common crystal oscillator with temperature compensation network, including crystal resonator, temperature compensation network With oscillating circuit module three part.Temperature compensation network, for compensating the skew of crystal oscillator frequency of oscillation under different temperatures, improves frequency Rate degree of stability；Oscillating circuit module provides negative resistance for crystal resonator, compensates crystal resonator energy loss in oscillatory process.

Crystal oscillator shown in Fig. 1 (a) is a closed loop system, its Induction Peried by circuit structure, integrated circuit technology, The impact of the factors such as the reasonability of temperature, parasitic parameter and circuit design.The Induction Peried of crystal oscillator to be made is little, needs Carefully design whole closed loop system.Meanwhile, in the crystal oscillator with direct compensation type temperature compensation network, during high temperature, temperature compensation Network makes the loss resistance of crystal resonator two ends equivalence increase, and the Induction Peried increase causing crystal oscillator even can not starting of oscillation. It addition, the randomness of integrated circuit technology causes the uncertainty of device parameters, more increase the difficulty of circuit design.

The starting of oscillation of crystal oscillator is an extremely complex process, and " negative resistance " that propose below as Vittoz analyzes method, Illustrate in conjunction with accompanying drawing 1.

According to " negative resistance " concept and nonlinear circuit analysis principle, the oscillating circuit module in crystal oscillating circuit can by its Equiva lent impedance Z at vibration fundamental frequency_c(1)Characterize, then the crystal oscillating circuit with temperature compensation network can be equivalent to shown in Fig. 1 (b) Structure, wherein Z_mIt it is the motional impedance of crystal resonator；L_q、R_q、C_qIt is the dynamic inductance of crystal resonator respectively, moves State loss resistance and dynamic capacity；C_TIt it is the load capacitance of crystal resonator under different temperatures；Z_c(1)It is that oscillating circuit module is at base Equiva lent impedance under frequency component；R_nIt is Z_c(1)The absolute value of real part.

In crystal oscillator self-oscillating, flow through the electric current I of crystal resonator_cBy initial current I₀It is gradually increased to circuit stability shake Electric current I when swinging_cs, during being somebody's turn to do, due to the non-linear effects of oscillating circuit module, equiva lent impedance Z of oscillating circuit module_c(1) With electric current I_cIncrease be gradually reduced.Work as Z_c(1)It is reduced to the absolute value R of its real part_nLoss resistance R with crystal resonator_qEqual Time, crystal oscillating circuit reaches stable oscillation stationary vibration state, and starting of oscillation completes.

The Induction Peried of crystal oscillator is the electric current I of crystal resonator_cFrom initial current I₀Electric current when increasing to circuit stability vibration I_csTime required for the 90% of amplitude, for calculating the Induction Peried of crystal oscillator, Yasuo Tsuzuk (Yasuo Tsuzuki, Takehiko Adachi and WJi en Zhang, Fast start-up crystal oscillator circuits, Frequency Control Symposium, 1995.49th.) etc. self-oscillating done certain simplification approximation, particularly as follows:

The self-oscillating of crystal oscillator is divided into three phases: the first stage is active device from power supply electrifying to oscillating circuit module The biasing of part reaches suitable direct current biasing point.This process duration t₁The shortest, the electric current flowing through crystal resonator is initial electricity Stream I₀, not changing over time, its size is

$I_0=V_t\·\sqrt{C_q/L_q}---\left(1\right)$

Wherein, C_qAnd L_qIt is dynamic capacity and the dynamic inductance of crystal, V_tIt is a powering up the initial voltage at rear crystal resonator two ends.

Second stage, the oscillation amplitude of crystal oscillator is the least, whole circuit can according to the analytical of small signal circuit, This process duration is the longest.In this stage, the electric current of crystal resonator is from initial current I₀Increase according to exponential form, the time Constant isThat is:

$I=I_0\exp \left(\frac{R_n-R_q}{2L_q}t\right)---\left(2\right)$

In formula, I is the electric current flowing through crystal resonator, and t is the time.The then time t required for this stage₂For:

$t_2=\frac{2L_q}{R_n-R_q}ln\left(\frac{I_1}{I_0}\right)---\left(3\right)$

Wherein I₁For flowing through the electric current of crystal resonator at the end of this stage.

Phase III, flow through the electric current I when electric current of crystal resonator progressively increases to stable oscillation stationary vibration_cs.This stage, crystal oscillating circuit Oscillation amplitude the biggest, it is necessary to the whole circuit of analytical of nonlinear circuit, the time required for this process is t₃。 Then the Induction Peried t of crystal oscillator is

T=t₁+t₂+t₃ (4)

Crystal oscillator energy fast start-up to be made, it is necessary to reduce t, owing to second stage persistent period in the self-oscillating of crystal oscillating circuit is the longest, The Induction Peried of crystal oscillator is typically reduced by reducing the time of second stage.It is logical that Yasuo Tsuzuki et al. proposes one Cross the initial current I increasing second stage₀The size method that reduces Induction Peried, but the method is only applicable to partial circuit The crystal oscillating circuit that structure is special.

More than analyze and show, the Induction Peried of crystal oscillator to be reduced, it is important to the timeconstantτ in second stage to be reduced₀.Typically, The Induction Peried of crystal oscillating circuit is 7～15 τ₀。

Summary of the invention

Long for existing crystal oscillator Induction Peried, the even shortcoming of not starting of oscillation when high temperature, the present invention utilizes the resistance of memristor It is worth continuously adjustable characteristic, it is provided that a kind of fast start-up crystal oscillator based on memristor.This crystal oscillator can be notable Increase the size of the equivalent negative resistance entered in terms of crystal resonator two ends, thus effectively reduce crystal oscillator in total temperature scope Interior Induction Peried, reduces the difficulty of crystal oscillating circuit design.

Time t needed for second stage in crystal oscillator self-oscillating₂For:

$t_2=\frac{2L_q}{R_n-R_q}ln\left(\frac{I_1}{I_0}\right)---\left(5\right)$

In formula, L_q, R_qIt is respectively dynamic inductance and the dynamic loss resistance of crystal；I₁, I₀It is crystal oscillating circuit self-oscillating respectively Electric current at the end of middle second stage and initial current；R_nIt it is the equivalent negative resistance of oscillating circuit module offer.

In theory, L is reduced_q、I₁、R_q, increase R_n、I₀The time t needed for second stage can be reduced₂.In reality, one Denier selectes the model of crystal resonator, L_q, R_qJust for definite value；And I₀Relevant to the structure of crystal oscillating circuit and biasing circuit, no Malleable；I₁Mainly by structure and the nonlinear property of active device of circuit, it is not easy to change.So crystal oscillator to be reduced The Induction Peried of circuit is it is necessary to increase the equivalent negative resistance R of oscillating circuit module_n。

Further, the parameter of the active devices such as the size of oscillating circuit module negative resistance and MOS or BJT, capacitance parameter and The resistance of memristor is correlated with.In theory, by adjusting the parameter of the active devices such as MOS or BJT, and electric capacity can be adjusted The Induction Peried making crystal oscillating circuit Deng the parameter of passive device is the shortest, but the parameter of the active device such as MOS or BJT in reality And integrated electric capacity is very sensitive to flow-route and temperature, circuit design stage is wayward；Other parasitic parameter is also more simultaneously Induction Peried is had an impact, increases the difficulty of circuit design.A kind of fast start-up crystal oscillator based on memristor of the present invention, Control to oscillating circuit module negative resistance size can be realized by the resistance adjusting memristor.Negative resistance is to memristor resistance R_mDepend on Bad property can be expressed as:

R_n=f (R_m) (6)

According to different semiconductor technology situations, adjust resistance R of memristor_m, make oscillating circuit module negative resistance R_nReach maximum R_n,max, thus the Induction Peried t of crystal oscillator minimizes value, it may be assumed that

R_n=f (R_m,opt)=R_n,max (7)

Technical scheme is as follows:

A kind of fast start-up crystal oscillator based on memristor, including crystal resonator, temperature compensation network and oscillating circuit module group The closed-loop path become；Crystal resonator is used for producing oscillator signal, temperature compensation network for compensate the frequency of oscillation of crystal resonator because of The skew that variations in temperature produces, oscillating circuit module is used for providing negative resistance, compensates crystal resonator energy in oscillatory process and damages Lose；It is characterized in that: oscillating circuit module is by the passive device such as active device, inductance capacitance and memristors such as BJT or MOS Network forms, and makes the equivalent negative resistance of oscillating circuit module increase by the resistance adjusting memristor, thus reduces rising of crystal oscillating circuit Shake the time.

Further, described memristor network is by m × n (m is the line number of memristor network, and n is the columns of memristor network) Memristor R_ij(i≥1,j≥1,R_ij>=0, i are line label, and j is row label) form through connection in series-parallel, in the control of internal erasable circuit Under system, meet the requirement that oscillating circuit module is the most variable to memristor resistance.

The invention have the benefit that oscillating circuit module includes the passive devices such as active device, inductance capacitance such as BJT or MOS And the memristor network being made up of m × n memristor, utilize the continuously adjustable characteristic of memristor resistance, by adjusting memristor Resistance, the negative resistance making oscillating circuit module is maximum, thus reduces the Induction Peried of crystal oscillator, it is achieved method is simple, can Strong operability；Different memristor values can be adjusted according to the characteristic of the active devices such as BJT or MOS in different semiconductor technologies, Process repeatability is good；Crystal oscillator with temperature compensation network is due to the equivalence loss electricity of crystal when temperature compensation network causes high temperature Resistance increases, and starting of oscillation difficulty or Induction Peried are long, owing to the resistance adjustability of memristor device is not limited by temperature, it is possible to achieve The fast start-up of crystal oscillator in the range of total temperature.

Accompanying drawing explanation

Fig. 1 (a) is the crystal oscillating circuit structured flowchart of existing band temperature compensation network, and (b) is its equivalent circuit diagram；

Fig. 2 is fast start-up crystal oscillator configuration block diagram based on memristor；

Fig. 3 (a) be based on memristor can the Colpitts crystal oscillator of fast start-up, (b) is its equivalent circuit diagram；

Fig. 4 is the equivalent negative resistance R of Colpitts crystal oscillator_nWith Induction Peried with memristor R_mThe simulation result of change.

Detailed description of the invention

A kind of fast start-up crystal oscillator based on memristor of the present invention is applicable to all of crystal oscillating circuit, does not limit to In a certain crystal oscillating circuit, the most for convenience of description, as a example by Colpitts crystal oscillating circuit, in conjunction with accompanying drawing 3 and attached Fig. 4 specifically states that the present invention realizes the embodiment of crystal oscillator fast start-up based on memristor.

Fig. 3 (a) be based on memristor can the Colpitts crystal oscillating circuit of fast start-up, this circuit by crystal resonator, Temperature compensation network and oscillating circuit module three part composition.The frequency that temperature compensation network produces because of variations in temperature for compensated crystal oscillator Skew, improves frequency stability；Oscillating circuit module is used for providing negative resistance.

Oscillating circuit module is by BJT pipe Q1, resistance Rb1, Rb2, electric capacity C1, C2, memristor network R_mComposition, wherein Resistance Rb1 and Rb2 provides direct current biasing, memristor network R to BJT pipe Q1_mFeedback circuit is formed with electric capacity C1, C2. The parameter of oscillating circuit module negative resistance is affected below in conjunction with its Analysis of Equivalent Circuit.

The plural oscillation equation of crystal oscillating circuit is:

g_mZ₁Z₃+Z₁+Z₂+Z₃=0 (8)

In formula, Z₁、Z₂And Z₃It is respectively BJT pipe Q1 colelctor electrode and emitter stage, colelctor electrode and basis set and basis set and emitter stage Between equiva lent impedance, g_mIt it is the mutual conductance of transistor BJT.

Equivalent circuit shown in 3 (b), Z with reference to the accompanying drawings₁、Z₂、Z₃Particularly as follows:

$Z_1=\frac{R_m\frac{1}{jwC1}}{R_m+\frac{1}{jwC1}}---\left(9\right)$

In formula, 1/jwC1 is the impedance of electric capacity C1.

$Z_2=\frac{\left(Rb1\right|\left|Rb2\right)(R_q+{\mathrm{jX}}_q+\frac{1}{{\mathrm{jwC}}_T})}{\left(Rb1\right|\left|Rb2\right)+R_q+{\mathrm{jX}}_q+\frac{1}{{\mathrm{jwC}}_T}}---\left(10\right)$

Wherein, X_qFor the equivalent reactance of crystal, CT is the equivalent capacity of temperature compensation network, 1/jwC_TIt is electric capacity C_TImpedance.

$Z_3=\frac{R_i\frac{1}{jwC2}}{R_i+\frac{1}{jwC2}}---\left(11\right)$

Wherein, R_iFor the input resistance of BJT pipe, 1/jwC2 is the impedance of electric capacity C2.So equation (8) can be written as:

$\begin{array}{c}\frac{g_{m0}}{1+jf/f_B}\·\frac{1-{\mathrm{jwR}}_{m}C1}{w^2{R}_{m}C{1}^2}\·\frac{1-{\mathrm{jwR}}_{i}C2}{w^2{R}_{i}C{2}^2}+\frac{1-{\mathrm{jwR}}_{m}C1}{w^2{R}_{m}C{1}^2}+\frac{1-{\mathrm{jwR}}_{i}C2}{w^2{R}_{i}C{2}^2}\\ +R_q+{(X_q-\frac{1}{{\mathrm{wC}}_T})}^2\frac{1}{Eb1\left|\right|Rb2}+j(X_q-\frac{1}{{\mathrm{wC}}_T})=0\end{array}---\left(12\right)$

In formula, g_m0Being the mutual conductance at low frequency of the BJT pipe, f is frequency, f_BIt it is unity gain bandwidth.The real part making above formula is Zero negative resistance obtaining oscillating circuit module is

$\begin{array}{c}{R}_n=\frac{g_{m0}}{\[1+{(f/f_{\mathrm{\β}})}^2\]w^{2}C1C2}(1+\frac{R_{m}C1+R_{i}C2}{{\mathrm{wR}}_m{R}_{i}C1C2}\·\frac{f}{f_{\mathrm{\β}}}-\frac{1}{w^2{R}_m{R}_{i}C1C2})\\ -\frac{1}{w^2{R}_{m}C{1}^2}\frac{1}{w^2{R}_{i}C{2}^2}-\frac{1}{Rb1\left|\right|Rb2}{(X_q-\frac{1}{{\mathrm{wC}}_T})}^2\end{array}---\left(13\right)$

It can be seen that the size of oscillating circuit negative resistance and BJT pipe mutual conductance g at frequency of oscillation_m, input resistance R_i, electric capacity C1, C2, biasing resistor Rb1, Rb2 and memristor network R_mRelevant.

In theory, by selecting suitable BJT device, thus parameter g can be adjusted_mWith input resistance R_i, and adjust electric capacity The value of C1, C2, the value of biasing resistor Rb1, Rb2 can make the Induction Peried of crystal oscillating circuit the shortest.

In reality, BJT device is relevant to selected semiconductor technology, and adjustable leeway is little.Electric capacity C1, C2 are to phase noise Impact very big, electric capacity to be realized is adjustable needs capacitor array, and the chip area taken is big, and cost is high.It addition, BJT Parameter and the integrated electric capacity of device are very sensitive to flow-route and temperature, and circuit design stage is wayward.Ic manufacturing process In other parasitic parameter also Induction Peried is had an impact, more increase the uncertainty of circuit design.

Owing to negative resistance is memristor network R_mWith the nonlinear function of biasing resistor Rb1, Rb2, by change biasing resistor Rb1, Rb2, memristor network R_mValue can realize the control to negative resistance.When circuit design parameter is reasonable, biasing resistor Rb1, Rb2 Impact on negative resistance is little.Change memristor network R_mValue can change the size of negative resistance.

The dependency of memristor resistance can be with function representation by negative resistance:

$\begin{array}{c}{R}_n=f\left(R_m\right)\\ =\frac{g_{m0}}{\[1+{(f/f_{\mathrm{\β}})}^2\]w^{2}C1C2}(1+\frac{R_{m}C1+R_{i}C2}{{\mathrm{wR}}_m{R}_{i}C1C2}\·\frac{f}{f_{\mathrm{\β}}}-\frac{1}{w^2{R}_m{R}_{i}C1C2})\\ -\frac{1}{w^2{R}_{m}C{1}^2}-\frac{1}{w^2{R}_{i}C{2}^2}-\frac{1}{Rb1\left|\right|Rb2}{(X_q-\frac{1}{{\mathrm{wC}}_T})}^2\end{array}---\left(14\right)$

According to g under different process and different temperatures_m0、R_i, the actual value of C1, C2, adjust R_m=R_m,optSo that:

$f^{\′}\left(R_m\right){|}_{R_{m,opt}}=0---\left(15\right)$

$f^{\&prime;\&prime;}\left(R_m\right){|}_{R_{m,opt}}<0---\left(16\right)$

Then R_n=f (R_m,opt)=R_n,max, the Induction Peried of crystal oscillating circuit is minimum.

Memristor network R_mIt is by m × n (m is the line number of memristor network, and n is the columns of memristor network) memristor R_ij(i≥1,j≥1,R_ij>=0, i are line label, and j is row label) formed by connection in series-parallel, all of R_ijBoth greater than zero corresponding to m × n The regular network of individual matrix composition, has R_ijEqual to zero corresponding to scramble network.Each memristor R_ijIt is internal with erasable circuit, Resistance continuously adjustabe can be easily carried out.

Fig. 4 be Fig. 3 (a) based on memristor can the simulation result of Colpitts crystal oscillating circuit of fast start-up, emulation Based on TSMC0.25um BCD technique, during emulation, crystal resonator uses resonant frequency to be equivalent parameters during 10M, Rb1 For 27k, Rb2 be 20k, C1 be 130pF, C2 be 160pF, VCC be 2.8V.The simulation result of Fig. 4 shows, when recalling Resistance device R_mTime less (50 Ω), negative resistance R_nThe least (14.92 Ω), now can not compensate crystal resonant due to crystal oscillating circuit module The energy loss of device, crystal oscillator not starting of oscillation；Along with memristor R_mResistance is continuously increased, negative resistance R_nIncrease, but increase to After certain value, negative resistance R_nStarting to reduce, Induction Peried also begins to increase.Can be seen that change memristor R_mValue can be effective Change size and the Induction Peried of negative resistance, and work as R_m=R_m,optDuring=300 Ω, negative resistance reaches maximum 559.4 Ω, crystal oscillating circuit Induction Peried minimize, for 977us, compared to less R_mInduction Peried (2.46ms) during value (100 Ω), subtracts Little by 60.28%, effect is obvious.

Above example is only the circuit implementation of the method reducing crystal oscillating circuit Induction Peried based on memristor of the present invention, this Invention is not limited only to Colpitts crystal oscillating circuit, and for the crystal oscillating circuit of other concrete forms, method of the present invention depends on The most effectively.All principles in the present invention, criterion, spirit and any amendment made within the scope of realizing circuit etc., equivalent, Equivalence change and improvement, should be included in the scope of the present invention.

Claims (2)

1. a fast start-up crystal oscillator based on memristor, including crystal resonator, temperature compensation network and oscillating circuit module The closed-loop path of composition；Crystal resonator is used for producing oscillator signal, and temperature compensation network is for compensating the frequency of oscillation of crystal resonator The skew produced because of variations in temperature, oscillating circuit module is used for providing negative resistance, compensates crystal resonator energy in oscillatory process Loss；It is characterized in that: oscillating circuit module includes active device, passive device and memristor network, adjust memristor Resistance makes the equivalent negative resistance of oscillating circuit module increase, thus reduces the Induction Peried of crystal oscillating circuit.

A kind of fast start-up crystal oscillator based on memristor, it is characterised in that: described memristor Device network is by m × n memristor R_ijForming through connection in series-parallel, under the control of internal erasable circuit, memristor network resistance is any Variable, wherein m is the line number of memristor network, and n is the columns of memristor network, and i is line label, and j is row label i≥1,j≥1,R_ij≥0。