CN1851486A - Method for determining inductive value of inductance for circuit chip - Google Patents

Abstract

The present invention adopts sub circle iteration average algorithm to calculate piece induction self-inductance value according to piece territory parameter, adopts whole average algorithm to calculate piece induction mutual inductance value, summarizing obtained self-inductance value with mutual inductance value to obtain said piece inductive induction value. Said method can determine induction value and territory parameter for different kinds of regular and irregular shape piece, reducing designing hardness and cycle for RF passive device and correlation circuit.

Description

Determine the method for the inductance value of inductance for circuit chip

Technical field

The present invention relates to a kind of method of inductance value of definite inductance for circuit chip, be specifically related in the radio communication passive device technical field on the sheet.

Background technology

On-chip spiral inductor is the critical elements in the wireless radiofrequency communication system, is widely used in each module of radio-frequency front-end, as module clocks such as RF preselection loop, low noise amplifier (LNA), voltage controlled oscillator (VCO) and LC loops.The on-chip inductor that adopts multilayer wiring to realize during the design radio frequency integrated circuit not only can reduce chip area, realizes monolithic radio frequency integrated circuit (RFIC), and can reduce the power consumption and the noise of circuit, thereby improves the performance of circuit.

Along with mobile communication develops to miniaturization, low power consumption, increasing to the demand of monolithic RFIC, on-chip inductor becomes the focus of domestic and international research in recent years.The inductance value parameter of on-chip inductor is relevant with multinomial structural parameters and technological parameter, thereby is difficult to accurately obtain inductance value by the known structure parameter, or draws the domain parameter by the inductance value of design.This increases integrated circuit (IC) design degree of accuracy, difficulty and cycle greatly.1974, Green House (Green person of outstanding talent this) proposed a kind of accurate algorithm and can try to achieve inductance value.This algorithm is divided into four section leads with every circle inductance, calculate the self-induction of every section lead respectively after stack obtain total self-induction.When calculating mutual inductance, obtain respectively the identical line of direction of current to positive mutual inductance and the line of current opposite in direction to negative mutual inductance, stack at last obtains total mutual inductance value.Self-induction and mutual inductance sum are the inductance value of on-chip inductor.When asking the self-induction of inductance, need 4n time, when calculating mutual inductance, calculate positive mutual inductance and need C _n ²Inferior, calculate negative mutual inductance and need 2n ²Inferior.According to Greenhouse (Green person of outstanding talent this) theory, inductance value L calculates and is divided into two parts: self-induction L _SelfWith mutual inductance M.

Greenhouse (Green person of outstanding talent this) formula is: L=Lself+M

Calculate self-induction L _SelfThe time, every circle inductance is divided into four sections conductors, calculate every section self-induction value L respectively ₀, stack at last.When the inductance of n circle calculates self-induction like this, need stack 4n time.Every section conductor self-induction formula is as follows

$L_0=0.002l[\ln \left(\frac{2l}{w+t}\right)+0.50049+\left(\frac{w+t}{3l}\right)]$

When calculating mutual inductance M, divide positive mutual inductance M ⁺, negative mutual inductance M ^-M ⁺Be the identical intersegmental mutual inductance of two conductor lines of direction of current, M ^-Be the intersegmental mutual inductance of two conductor lines of current opposite in direction.Formula is as follows:

M＝M ^-+M ⁺

M ^-，M ⁺＝2lQ

$Q=\ln [\frac{l}{\mathrm{GMD}}+\sqrt{1+\frac{l^2}{{\mathrm{GMD}}^2}}-\sqrt{1+\frac{{\mathrm{GMD}}^2}{l^2}}+\frac{\mathrm{GMD}}{l}]$

Wherein l is the length of every section conductor.This algorithm is comparatively accurate, but very loaded down with trivial details, efficient is not high, and along with the increase of number of inductor, can increase by exponentially the operation time of algorithm, is not easy to practical design and uses.

1999, Stanford University proposed Wheeler (Weir is reined in) formula, electric current approximate formula and numerical value and has fitted formula and calculate on-chip inductor.These three kinds of closed formulas can directly obtain inductance value by the part domain parameter of on-chip inductor.Algorithm is more accurate, and simple and effective, and the designer can directly estimate inductance value from the domain parameter of inductance.But algorithm can only calculate live width and spacing is the structure and the domain parameter on-chip inductor within the specific limits of constant, the domain parameter area is inductance outside diameter d out=100～480 μ m, live width w=2 μ m～0.3dout, distance between centers of tracks s=2～3 μ m, inductance inner diameter d in=0.1～0.9dout, the on-chip inductor that algorithm is suitable for is limited in scope underaction.

Summary of the invention

The technical matters that the method for the inductance value of definite inductance for circuit chip of the present invention will solve is to release a kind of branch circle based on the domain parameter to iterate algorithm, can accurately calculate the inductance value of on-chip inductor fast, the regular shape inductance such as routine is square except that can be used for, hexagon, this method also can be used for irregularly shaped on-chip inductor analysis as the gradual change of live width spacing, thereby has simplified the design difficulty of on-chip inductor.

The method of the inductance value of definite inductance for circuit chip of the present invention is according to the domain parameter on the sheet, adopt and divide circle to iterate average algorithm calculating on-chip inductor self-induction value, adopt ensemble average algorithm computation on-chip inductor mutual inductance value, will obtain the inductance value that described on-chip inductor is tried to achieve in self-induction value and the addition of mutual inductance value again.

Wherein, described domain parameter comprises: inductance inner diameter d in, and number of turns n, the number of turns rounds Ni, live width w, distance between centers of tracks s, metal layer thickness t, the wide w of every astragal _i, i encloses the distance between centers of tracks s of i+1 circle _i

The branch circle of described calculating on-chip inductor self-induction value iterates average algorithm and comprises the steps:

(1) utilizes the symmetry characteristic of inductance, inductance is divided into plurality of sections according to inductance inner diameter d in, live width w and distance between centers of tracks s sum;

(2) determine the length l of every circle inductance _Quan(i) round Ni, the wide w of every astragal with inductance inner diameter d in, number of turns n, the number of turns _i, i encloses the distance between centers of tracks S of i+1 circle _iLinear relationship, calculate the length l of every circle inductance _Quan(i);

(3) calculate every circle inductance self-induction value L _Quan(i);

(4) every circle self-induction value is superimposed.

Wherein, calculate the length l of every circle inductance _Quan(i), use following formula:

l _quan(i)＝f(din，w _i，s _i，Ni)。

Calculate the self-induction value L of every circle inductance _Quan(i), use following formula:

$L_{\mathrm{quan}}\left(i\right)={2l}_{\mathrm{quan}}(\ln \frac{l_{\mathrm{quan}}\left(i\right)}{n(w+t)}-0.2).$

On-chip inductor self-induction value L is obtained in calculating _Total, use following formula:

$L_{\mathrm{total}}=\underset{i=1}{\overset{\mathrm{Ni}}{\mathrm{\Σ}}}{L}_{\mathrm{quan}}\left(i\right).$

The ensemble average algorithm of described calculating on-chip inductor mutual inductance value comprises the steps:

(1) by the length overall l of every circle inductance _Quan(i) obtain the average length l of every section conductor _{On average}

(2) according to l _{On average}Value calculates average positive mutual inductance M ⁺Value with average negative mutual inductance M.

Wherein, the average length l of every section conductor of described calculating _{On average}Comprise the steps:

(1) by the length l of every circle inductance _Quan(i) the total length l of calculating inductance leads _Total, use following formula:

l _total＝f(l _quan(i)，din，w _i，s _i)；

(2) by the total length l of inductance leads _Total/ 4n obtains the average length l of every section conductor _{On average}, use following formula:

l _{On average}=f (l _Total, n).

In the process of calculating the mutual inductance value, the intersegmental interaction of the parallel wire of current opposite in direction is approximately 2n ², mean distance GMD is approximately lead average length l between the conducting line segment of negative mutual inductance effect _{On average}

On the basis of calculating square inductance, try to achieve the different girth ratio of non-square inductance respectively, be used to calculate the inductance value of non-square inductance.

The method of the inductance value of definite inductance for circuit chip of the present invention is a unit with every circle inductance when asking the self-induction of inductance, obtain the mean value of conductor length in every circle inductance after, iterate and obtain total self-induction value.Then the on-chip inductor of n circle only need calculate n time.When calculating mutual inductance, adopt the ensemble average algorithm, demand goes out the inductance total length, can try to achieve positive and negative mutual inductance, shorten computing time, simultaneously, this method can be in conjunction with the domain technological parameter of reality, recently realize the computing of any irregular contour on-chip inductor realizing the calculating of required different shape inductance by the girth of phase square shaped, reduce the design difficulty and the cycle of radio frequency passive device and interlock circuit.

Description of drawings

Figure 1A is square inductance parameters structure vertical view;

Figure 1B is a hexagon inductance parameters structure vertical view;

Fig. 1 C is an octagon inductance parameters structure vertical view;

Fig. 2 is through the square inductance parameters structure vertical view after dividing;

Fig. 3 is the program flow diagram of method of the inductance value of definite inductance for circuit chip of the present invention.

Embodiment

Now in conjunction with the accompanying drawings the embodiment of the method for inductance for circuit chip value of the present invention is further described.

Structure inductor design such as square, octagon, regular hexagon and circle have been realized according to this method.Its crucial domain parameter is illustrated in figure 1 as outside diameter d out, inner diameter d in, number of turns n, the number of turns rounds Ni, live width w, distance between centers of tracks s, metal layer thickness t.

As shown in Figure 2, utilize the symmetry characteristic of inductance, inductance is divided into plurality of sections according to inductance inner diameter d in, live width w and distance between centers of tracks s sum (w+s).

The total inductance value L of on-chip inductor should be made up of self-induction Lself and mutual inductance M two parts:

L＝Lself+M (1)

Wherein the self-induction value is:

$\mathrm{Lself}=0.002l[\ln \left(\frac{2l}{w+t}\right)+0.50049+\left(\frac{w+t}{3l}\right)]---\left(2\right)$

The mutual inductance value is positive mutual inductance M ⁺With negative mutual inductance M ^-And:

M＝M ^-+M ⁺

M ^-，M ⁺＝2lQ

$Q=\ln [\frac{l}{\mathrm{GMD}}+\sqrt{1+\frac{l^2}{{\mathrm{GMD}}^2}}-\sqrt{1+\frac{{\mathrm{GMD}}^2}{l^2}}+\frac{\mathrm{GMD}}{l}]---\left(3\right)$

L is the length of conducting line segment in formula (2), (3), and GMD is the spacing of any two section leads.

The flow process of the algorithm of inductance for circuit chip value of the present invention as shown in Figure 3.

The algorithm of inductance for circuit chip value of the present invention is a unit with every circle inductance, at first determines designed on-chip inductor structure and domain parameter, as inductance outside diameter d out, and inner diameter d in, number of turns n, the number of turns rounds Ni, the wide w of every astragal _i, i encloses the distance between centers of tracks s of i+1 circle _i, metal layer thickness t then calculates the length overall l of every circle inductance _Quan(i), obtain the average length of every section inductance again.Utilize formula (2) to obtain every circle inductance self-induction value L then _Quan(i).Specific as follows:

$l_{\mathrm{quan}}\left(1\right)=3.5\mathrm{din}+7\underset{i=1}{\overset{\mathrm{Ni}}{\mathrm{\Σ}}}(\frac{w_i+w_{i+1}}{2}+s_i)-(\frac{w_1+w_2}{2}+s_1)$

$l_{\mathrm{quan}}\left(i\right)=4\mathrm{din}+8\underset{i=2}{\overset{\mathrm{Ni}}{\mathrm{\Σ}}}(\frac{w_i+w_{i+1}}{2}+s_i)-(\frac{w_i+w_{i+1}}{2}+s_i)+\frac{w_i+w_{i+1}}{2}+s_{i-1}$

$\mathrm{din}=\mathrm{dout}-w_1-2\left(\mathrm{\Σ}(\frac{w_i+w_{i+1}}{2}+s_i)\right)$

$L_{\mathrm{quan}}\left(i\right)=2l_{\mathrm{quan}}(\ln \frac{l_{\mathrm{quan}}\left(i\right)}{n(w+t)}-0.2)$

Iterate at last and obtain total self-induction value L _Total:

$L_{\mathrm{total}}=\underset{i=1}{\overset{\mathrm{Ni}}{\mathrm{\Σ}}}{L}_{\mathrm{quan}}\left(i\right)$

When asking mutual inductance, adopt the ensemble average algorithm of inductance mutual inductance value.According to the symmetry of induction structure, done following approximate: the intersegmental interaction of the parallel wire of current opposite in direction is 2n ²Mean distance GMD is approximately lead average length l between the conducting line segment of negative mutual inductance effect _{On average}

At first by the length l of every circle inductance _Quan(i) the total length l of calculating inductance leads _Total, and by the total length l of inductance leads _TotalObtain the average length l of every section conductor _{On average}

Use following formula: l _Total=f (l _Quan(i), din, w _i, s _i);

l _{On average}=l _Total/ 4n;

Then according to l _{On average}Value calculates average positive mutual inductance M ⁺Value with average negative mutual inductance M.

When n is integer, $l_{\mathrm{total}}=l_{\mathrm{quan}}\left(1\right)+\underset{i=2}{\overset{\mathrm{Ni}}{\mathrm{\Σ}}}{l}_{\mathrm{quan}}\left(i\right)+0.5\mathrm{din}+(w_{\mathrm{Ni}}+s_{\mathrm{Ni}})$

When n is not integer, $l_{\mathrm{total}}=l_{\mathrm{quan}}\left(1\right)+\underset{i=2}{\overset{\mathrm{Ni}}{\mathrm{\Σ}}}{l}_{\mathrm{quan}}\left(i\right)+2.5\mathrm{din}+(w_{\mathrm{Ni}}+s_{\mathrm{Ni}})$

M ^-≈0.467nl _total

$M^{+}\≈2l_{\mathrm{total}}(n-1)\ln [\sqrt{1+{\left(\frac{l_{\mathrm{total}}}{4\mathrm{nd}}\right)}^2}+\frac{l_{\mathrm{total}}}{4\mathrm{nd}}-\sqrt{1+{\left(\frac{4\mathrm{nd}}{l_{\mathrm{total}}}\right)}^2}+\frac{4\mathrm{nd}}{l_{\mathrm{total}}}]$

$d=(w+s)\frac{(3n-2\mathrm{Ni}-1)(\mathrm{Ni}+1)}{3(2n-\mathrm{Ni}-1)}$

D is a mean distance between the identical parallel wire of direction of current.

On the basis of calculating square inductance, try to achieve the different girth ratio of non-square inductance respectively, be used to calculate the inductance value of non-square inductance.

At last positive and negative mutual inductance and self-induction addition are obtained the inductance value of integrated circuit.

According to flow process shown in Figure 3, can carry out the corresponding program design.Determine designed on-chip inductor structure and domain parameter, as inductance outside diameter d out, inner diameter d in, number of turns n, the number of turns rounds Ni, the wide w of every astragal _i, i encloses the distance between centers of tracks s of i+1 circle _i, metal layer thickness t, and utilize the aforementioned calculation method just can draw the inductance value of inductance.

Claims (10)

1, a kind of method of inductance value of definite inductance for circuit chip, it is characterized in that: according to the domain parameter on the sheet, adopt and divide circle to iterate average algorithm calculating on-chip inductor self-induction value, adopt ensemble average algorithm computation on-chip inductor mutual inductance value, will obtain the inductance value that described on-chip inductor is tried to achieve in self-induction value and the addition of mutual inductance value again.

2, the method for the inductance value of definite inductance for circuit chip according to claim 1 is characterized in that: described domain parameter comprises: inductance inner diameter d in, and number of turns n, the number of turns rounds Ni, live width w, distance between centers of tracks s, metal layer thickness t, the wide w of every astragal _i, i encloses the distance between centers of tracks s of i+1 circle _i

3, the method for the inductance value of definite inductance for circuit chip according to claim 1 is characterized in that: the branch circle of described calculating on-chip inductor self-induction value iterates average algorithm and comprises the steps:

(1) utilizes the symmetry characteristic of inductance, inductance is divided into plurality of sections according to inductance inner diameter d in, live width w and distance between centers of tracks s sum;

(2) determine the length l of every circle inductance _Quan(i) round Ni, the wide w of every astragal with inductance inner diameter d in, number of turns n, the number of turns _i, i encloses the distance between centers of tracks s of i+1 circle _iLinear relationship, calculate the length l of every circle inductance _Quan(i);

(3) calculate every circle inductance self-induction value L _Quan(i);

(4) every circle self-induction value is superimposed.

4, the method for the inductance value of definite inductance for circuit chip according to claim 3 is characterized in that: the length l of calculating every circle inductance _Quan(i), use following formula:

l _quan(i)＝f(din，w _i，s _i，Ni)。

5, the method for the inductance value of definite inductance for circuit chip according to claim 3 is characterized in that: the self-induction value L that calculates every circle inductance _Quan(i), use following formula:

$L_{\mathrm{quan}}\left(i\right)=2l_{\mathrm{quan}}(\ln \frac{l_{\mathrm{quan}}\left(i\right)}{n(w+t)}-0.2).$

6, the method for the inductance value of definite inductance for circuit chip according to claim 3 is characterized in that: calculate on-chip inductor self-induction value L _Total, use following formula:

$L_{\mathrm{total}}=\underset{i=1}{\overset{\mathrm{Ni}}{\mathrm{\Σ}}}{L}_{\mathrm{quan}}\left(i\right).$

7, the method for the inductance value of definite inductance for circuit chip according to claim 1 is characterized in that: the ensemble average algorithm of described calculating on-chip inductor mutual inductance value comprises the steps:

(1) by the length overall l of every circle inductance _Quan(i) obtain the average length l of every section conductor _{On average}

(2) according to l _{On average}Value calculates average positive mutual inductance M ⁺With average negative mutual inductance M ^-Value.

8, the method for the inductance value of definite inductance for circuit chip according to claim 7 is characterized in that: the average length l of every section conductor of described calculating _{On average}Comprise the steps:

(1) by the length l of every circle inductance _Quan(i) the total length l of calculating inductance leads _Total, use following formula:

l _total＝f(l _quan(i)，din，w _i，s _i)；

(2) by the total length l of inductance leads _Total/ 4n obtains the average length l of every section conductor _{On average}, use following formula:

l _{On average}=f (l _Total, n).

9, according to the method for the inductance value of claim 1 or 2 or 3 or 7 described definite inductance for circuit chip, it is characterized in that: in the process of calculating the mutual inductance value, the intersegmental interaction of the parallel wire of current opposite in direction is approximately 2n ², mean distance GMD is approximately lead average length l between the conducting line segment of negative mutual inductance effect _{On average}

10, according to the method for the inductance value of claim 1 or 2 or 3 or 7 described definite inductance for circuit chip, it is characterized in that: on the basis of calculating square inductance, try to achieve the different girth ratio of non-square inductance respectively, be used to calculate the inductance value of non-square inductance.

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