CN103957000A - Small-signal analysis method for analog integrated circuit of MOS transistor - Google Patents

Abstract

The invention discloses a small-signal analysis method for an analog integrated circuit of an MOS transistor. According to the method, the MOS transistor is abstracted to a multiterminal amplifier, an impedor forming an amplifying circuit with the multiterminal amplifier is abstracted to a multiterminal feedback loop, and the multiterminal amplifier and the multiterminal feedback loop form an integrated multiterminal small-signal control and feedback system. A matrix calculation method is adopted for analysis of relations among multiterminal parameters of input signals, output signals, feedback signals, net input signals, amplification coefficients and feedback coefficients of the amplifying circuit formed by the MOS transistor. Small-signal analysis calculation and analysis can be carried out on the analog integrated circuit from the perspective of system angles, small-signal parameters such as a transfer function, input impedance and output impedance of the analog integrated circuit are solved fast, and the method has the advantages of being simple in step and high in calculation efficiency.

Description

A kind of small-signal analysis method for MOS transistor analog integrated circuit

Technical field

The present invention relates to signal analysis research field, particularly a kind of small-signal analysis method for MOS transistor analog integrated circuit.

Background technology

Along with the fast development of integrated circuit industry, MOS transistor is with low cost, superior performance and being widely used in analog integrated circuit design.Along with technique is constantly progressive, MOS transistor channel length is shorter and shorter, the second-order effects of MOS transistor is become and can not ignore, and becomes the key factor that affects circuit performance.Existing analog integrated circuit small-signal analysis method is first to draw AC small signal equivalent circuit, then lists electric current and voltage by Kirchhoff's law and expresses formula, finally solves output signal, gain, input and output impedance etc.Along with increasing and the increase of analog integrated circuit scale of MOS transistor second-order effects, the calculating of this traditional small-signal analysis method becomes increasingly complex, its circuit topology is difficult to from system perspective analysis, thereby it is abstract and provide Integrative expression formula to be difficult to system, make circuit analysis have certain blindness, optimized efficiency is low.

Summary of the invention

Main purpose of the present invention is that the shortcoming that overcomes prior art is with not enough, a kind of small-signal analysis method for MOS transistor analog integrated circuit is provided, the method proposes from system perspective, analog integrated circuit to be carried out calculating and the analysis of small-signal, has advantages of that step is simple, computational efficiency is high.

Object of the present invention realizes by following technical scheme: a kind of small-signal analysis method for MOS transistor analog integrated circuit, comprises the following steps:

(1) extract multiport amplifier model.Multiport amplifier model, taking MOS transistor multiport amplifier as basis, and is expanded with this.For example symmetrical difference MOS transistor can be abstracted into multiport amplifier, or MOS transistor cascade is abstracted into multiport amplifier.MOS transistor multiport amplifier model is as follows: by the small-signal drain-source current i in MOS transistor _dbe expressed as amplification coefficient vector with small-signal control voltage vector product, wherein, g _mto change the amplification coefficient causing, g by grid voltage _mbthe amplification coefficient being caused by body bias effect, g _mbit is the amplification coefficient being caused by channel-length modulation; v _gsrepresent the added small signal in two ends, MOS transistor grid source, v _bsrepresent the added small signal in MOS transistor lining two ends, source, v _dsrepresent the added small signal in MOS transistor drain-source two ends.

(2) determine multiterminal input signal and feedback factor matrix.Disconnect feedback, analyze multiport amplifier input signal.Impact according to other elements of Output Signal Analysis system on multiport amplifier net input signal, determines feedback factor matrix.

(3), according to multiterminal control reponse system model, output signal matrix can be used input signal matrix, amplification coefficient matrix, feedback factor matrix notation.Multiterminal control reponse system model a: Circuits System is equivalent to M input and N output; M input end signal amplifies through multiport amplifier A, and the output signal of N output, through multiple feedback loop F, forms feedback summation signals GS at input, and the stack of feedback summation signals and input signal forms the net input signal D of multiport amplifier A; If M input (I ₁, I ₂..., I _m) formation input signal matrix [I], N output (O ₁, O ₂..., O _n) formation output signal matrix [O]; Output signal matrix [O] is the multiterminal feedback loop of M × N matrix [F] through a feedback factor, forms feedback summation matrix [GS] at M input; This feedback summation matrix [GS] forms net input signal matrix [D] with input signal matrix [I] stack; Amplification coefficient is that multiport amplifier and the multiterminal feedback loop of N × Metzler matrix [A] forms MOS transistor multiterminal small-signal closed-loop system; [E] representation unit matrix, the pass between each multiterminal signal is: [O]=([E]+[A] [F]) ^-1[A] [I].

(4) according to the definition of each small-signal parameter, utilize output signal, can go out the small-signal parameters such as gain, input impedance, output impedance by rapid solving.

Compared with prior art, tool has the following advantages and beneficial effect in the present invention:

1, the present invention only need analyze the feedback factor of circuit, just can obtain fast the small-signal parameters such as the small signal gain, input impedance, output impedance of circuit.And adopt traditional solution, and need draw small-signal equivalent circuit figure, and list a series of equations and solve, its step complexity and computational efficiency are lower.

2, small-signal analysis method proposed by the invention, with the abstract angle of system, circuit to be analyzed, so can utilize system feedback theory, according to the variation of amplification coefficient and feedback factor, analyze intuitively the situation of change of circuit performance in the time that component parameters changes.And traditional analytical method can not analyze the variation of circuit performance intuitively, can only first solve circuit small-signal expression formula, the impact on circuit performance obtain component parameters variation from expression formula time.

Brief description of the drawings

Fig. 1 is MOS transistor small-signal multiterminal control model schematic diagram in the present invention;

Fig. 2 is MOS transistor amplifying circuit small-signal multiterminal control feedback model schematic diagram of the present invention;

Fig. 3 is the schematic diagram that MOS transistor amplifying circuit is asked voltage gain;

Fig. 4 is the tradition of circuit shown in Fig. 3 small-signal equivalent circuit figure;

Fig. 5 is the schematic diagram that MOS transistor amplifying circuit is asked output impedance;

Fig. 6 is the tradition of circuit shown in Fig. 5 small-signal equivalent circuit figure.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment 1

The present embodiment is mainly to propose a kind of small-signal analysis method for MOS transistor analog integrated circuit, specifically proposes respectively MOS transistor small-signal multiterminal control model and MOS transistor amplifying circuit small-signal multiterminal control feedback model.In ac small signal situation, MOS transistor is abstracted into a multiport amplifier by this method, the impedance component that forms amplifying circuit together with multiport amplifier is abstracted into multiterminal feedback loop, and multiport amplifier and multiterminal feedback loop form the complete control of multiterminal small-signal and a reponse system.Relation between the multiterminal parameters such as model adopts matrix computations method, input signal, output signal, feedback signal, net input signal, amplification coefficient and the feedback factor of the amplifying circuit that MOS transistor is formed is analyzed.The feature of this model is to carry out from system perspective calculating and the analysis of small-signal to analog integrated circuit, and rapid solving goes out transfer function, the input impedance of analog integrated circuit, the small-signal parameters such as output impedance.

Fig. 1 is MOS transistor small-signal multiterminal control model schematic diagram of the present invention.According to semiconductor device physics, MOS transistor drain-source current I _dcan be expressed as:

I _d=f(V _gs,V _bs,V _ds)

Wherein V _gsrepresent the voltage at two ends, MOS transistor grid source; V _bsrepresent the voltage at MOS transistor lining two ends, source; V _dsrepresent the voltage at MOS transistor drain-source two ends.

The variation of considering each signal is that the relation between small-signal has:

i _d=g _m*v _gs+g _mb*v _bs+g _md*v _ds

Wherein $g_m=\frac{{\∂I}_d}{{\∂V}_{\mathrm{gs}}},g_{\mathrm{mb}}=\frac{{\∂I}_d}{{\∂V}_{\mathrm{bs}}},g_{\mathrm{mb}}=\frac{{\∂I}_d}{{\∂V}_{\mathrm{ds}}}$ Represent respectively output drain-source current signal I _dto V _gs, V _bsand V _dscontrol the partial derivative of voltage signal variable for these three.V in Fig. 1 _gsrepresent the added small signal in two ends, MOS transistor grid source, v _bsrepresent the added small signal in MOS transistor lining two ends, source, v _dsrepresent the added small signal in MOS transistor drain-source two ends.With vector can be by MOS transistor drain-source small-signal current i _dbe expressed as:

Wherein amplification coefficient vector control signal vector gm changes the amplification coefficient causing, g by grid voltage _mbthe amplification coefficient being caused by body bias effect, g _mbit is the amplification coefficient being caused by channel modulation effect.

Fig. 2 is the MOS transistor amplifying circuit small-signal multiterminal control feedback model schematic diagram that the present invention proposes.M input (I in this multiterminal control feedback model ₁, I ₂..., I _m) formation input signal matrix [I], N output (O ₁, O ₂..., O _n) formation output signal matrix [O]; Output signal matrix [O] is the multiterminal feedback loop of M × N matrix [F] through a feedback factor, forms M × N feedback matrix [G], wherein G at input end _mmrepresent n output signal, through F _nfeedback loop, the feedback signal forming at m input; N output signal is through feedback loop, and forming feedback signal summation at m input is GS _m, the feedback signal summation (GS of M input end ₁, GS ₂..., GS _m) form and feed back summation matrix [GS]; This feedback summation matrix [GS] forms net input signal matrix [D] with input signal matrix [I] stack; Amplification coefficient is that multiport amplifier and the multiterminal feedback loop of N × Metzler matrix [A] forms MOS transistor multiterminal small-signal closed-loop system.

Carry out mathematical derivation with regard to multiterminal control feedback model below: (illustrate: wherein [] representing matrix; [] ^trepresent transposed matrix; [] ^-1represent inverse matrix; [E] representation unit matrix, [E]=[E] _nNN)

[I] represents input signal matrix, [I]=[I] _mMM=[I ₁i ₂i _m] ^t;

[O] represents output signal matrix, [O]=[O] _nNN=[O ₁o ₂o _n] ^t;

[D] represents net input signal matrix, [D]=[D] _mMM=[D ₁d ₂d _m] ^t;

[GS] represents feedback summation matrix, [GS]=[GS] _mMM=[GS ₁gS ₂gS _m] ^t; Wherein GS _m=G _m1+ G _m2+ ...+G _mN, represent that N output is through feedback loop, the feedback signal summation forming at m input.

[A] represents amplification coefficient matrix, wherein Anm, represents m amplification coefficient that inputs to n output.

[F] represents degeneration factor matrix, wherein [F _n]=[F _1nf _2nf _mM] ^t, represent n output signal through the degeneration factor vector of feedback loop.

Have according to definition:

Output signal: [O]=[A] [D]

Feedback signal: [GS]=-[F] [O]

Net input signal: [D]=[I]+[GS]

Solve Integrative expression formula:

[O]=([E]+[A][F]) ^-1[A][I]

Fig. 3 is that MOS transistor amplifying circuit is asked voltage gain schematic diagram.As shown in Figure 3, this circuit is MOS transistor common source amplifying circuit.Below to adopt the voltage gain solution procedure of analytical method of the present invention to amplifying circuit shown in Fig. 3:

(1): extract multiport amplifier model: MOS transistor is abstracted into multiport amplifier, amplification coefficient vector control signal (net input signal) vector be output as Single-end output, i.e. output signal [O]=id.

(2): determine multiterminal input signal and feedback factor matrix: in the situation that not considering feedback, in the situation of short circuit feedback resistance Rs and RD, only have v _gsthere is input signal Vin, v _bs, v _dsbe and exchange ground connection, therefore multiterminal input signal vector is output signal i _sthrough resistance R _s, make multiport amplifier v _gs, v _bs, v _dsend net input signal reduces, output signal i _dthrough resistance R _dmake v _dsend net input signal reduces, therefore degeneration factor vector

(3): according to multiterminal control reponse system model, solve output signal:

$\begin{array}{c}{i}_d=\left[o\right]={\left(\right[E]+[A\left]\right[F\left]\right)}^{-1}\left[A\right]\left[I\right]=\frac{\stackrel{\→}{A}\stackrel{\→}{\mathrm{Vin}}}{1+\stackrel{\→}{A}\stackrel{\→}{F}}\\ =\frac{g_m\mathrm{Vin}}{1+g_m{R}_S+g_{\mathrm{mb}}{R}_S+g_{\mathrm{mb}}(R_D+R_S)}\end{array}$

(4): according to voltage gain definition, utilize output signal to solve voltage gain expression formula:

$\mathrm{Av}=\frac{\mathrm{Vout}}{\mathrm{Vin}}=\frac{-i_d{R}_D}{\mathrm{Vin}}=\frac{{-g}_m{R}_D}{1+g_m{R}_s+g_{\mathrm{mb}}{R}_s+g_{\mathrm{mb}}(R_D+R_s)}$

Fig. 4 is small-signal equivalent circuit figure circuit shown in Fig. 3 being drawn with reference to classical analog integrated circuit small-signal analysis books [Behzad Razavi, analog CMOS integrated circuit design (process plate), publishing house of Tsing-Hua University, 2005].

In small-signal equivalent circuit as shown in Figure 4, flow through R _selectric current with flow through R _dsize of current equate, opposite direction, the source lining bias voltage Vsb=-Vbs of MOS transistor is identical with the voltage on resistance R S, is all therefore

To the input circuit Kirchhoff's second law in the small-signal equivalent circuit shown in Fig. 4, can obtain

$V_1=V_{\mathrm{in}}+\frac{\mathrm{Vout}*\mathrm{Rs}}{R_D}.$

If flowing through the electric current of output impedance ro is I _ro, the output node in the small-signal equivalent circuit figure shown in Fig. 4 being used to Kirchhoff's current law (KCL), can obtain

$\begin{array}{c}{I}_{\mathrm{ro}}=-\frac{\mathrm{Vout}}{R_D}-(g_m{V}_1+g_{\mathrm{mb}}{V}_{\mathrm{bs}})\\ =-\frac{\mathrm{Vout}}{R_D}-[g_m(V_{\mathrm{in}}+\frac{\mathrm{Vout}*\mathrm{Rs}}{R_D})+g_{\mathrm{mb}}\frac{\mathrm{Vout}*\mathrm{Rs}}{R_D}]\end{array}$

Use Kirchhoff's second law, R at output loop _sshould equal Vout with the pressure drop sum on ro, so

$\mathrm{Vout}=I_{\mathrm{ro}}*\mathrm{ro}-\frac{\mathrm{Vout}}{R_D}*\mathrm{Rs}$

$=-\frac{\mathrm{Vout}}{R_D}*\mathrm{ro}-[g_m(V_{\mathrm{in}}+\frac{\mathrm{Vout}*\mathrm{Rs}}{R_D})+g_{\mathrm{mb}}\frac{\mathrm{Vout}*\mathrm{Rs}}{R_D}*\mathrm{ro}-\frac{\mathrm{Vout}}{R_D}*\mathrm{Rs}$

Draw thus circuit small signal gain

$\begin{array}{c}\mathrm{Av}=\frac{\mathrm{Vout}}{V_{\mathrm{in}}}=\frac{-g_m{R}_D\mathrm{ro}}{R_D+R_S+\mathrm{ro}+(g_m+g_{\mathrm{mb}})R_S\mathrm{ro}}\\ =\frac{-g_m{R}_D}{1+R_D/\mathrm{ro}+R_S/\mathrm{ro}+(g_m+g_{\mathrm{mb}})R_S}\end{array}$

When MOS transistor is operated in saturation region, have substitution above formula can obtain

$\mathrm{Av}=\frac{-g_m{R}_D}{1+g_m{R}_S+g_{\mathrm{mb}}{R}_S+g_{\mathrm{mb}}(R_D+R_S)}$

Fig. 5 is that MOS transistor amplifying circuit is asked output impedance schematic diagram.As shown in Figure 5, this circuit is that MOS transistor common source amplifying circuit is asked output impedance schematic diagram.Below to adopt the output impedance solution procedure of analytical method of the present invention to amplifying circuit shown in Fig. 5:

(1): extract multiport amplifier model: MOS transistor is abstracted into multiport amplifier, amplification coefficient vector control signal (net input signal) vector be output as Single-end output, i.e. output signal [O]=i _d.

(2): determine multiterminal input signal and feedback factor matrix: in the situation that not considering feedback, in the situation of short circuit feedback resistance Rs, only have v _dsthere is input signal V _x, v _gs, v _bsbe and exchange ground connection, therefore multiterminal input signal vector is output signal i _sthrough resistance R _s, make multiport amplifier v _gs, v _bs, v _dsend net input signal all reduces, therefore degeneration factor vector

(3): according to multiterminal control reponse system model, solve output signal:

$i_d=\left[o\right]={\left(\right[E]+[A\left]\right[F\left]\right)}^{-1}\left[A\right]\left[I\right]=\frac{\stackrel{\→}{A}\stackrel{\→}{V}\mathrm{in}}{1+\stackrel{\→}{A}\stackrel{\→}{F}}=\frac{g_{\mathrm{mb}}{V}_x}{1+g_m{R}_S+g_{\mathrm{mb}}{R}_S+g_{\mathrm{mb}}{R}_S}$

(4): according to output impedance definition, utilize output signal to solve gain expressions:

$R_{\mathrm{out}}=\frac{\mathrm{Vx}}{i_d}=\frac{(1+\stackrel{\→}{A}\stackrel{\→}{F})}{g_{\mathrm{mb}}}=\frac{1+(g_m+g_{\mathrm{mb}}+g_{\mathrm{md}})R_S}{g_{\mathrm{md}}}$

Fig. 6 is small-signal equivalent circuit figure circuit shown in Fig. 5 being drawn with reference to classical analog integrated circuit small-signal analysis books (Behzad Razavi, analog CMOS integrated circuit design (process plate), publishing house of Tsing-Hua University, 2005).

In small-signal equivalent circuit as shown in Figure 6, flow through R _selectric current equal i _d, the input circuit Kirchhoff's second law in small-signal equivalent circuit, can obtain

V ₁=-i _dR _S

The source lining bias voltage V of MOS transistor _sb=-V _bswith resistance R _son voltage identical, therefore V _bs=V ₁; If flowing through the electric current of output impedance ro is I _ro, the output node in the small-signal equivalent circuit figure shown in Fig. 6 being used to Kirchhoff's current law (KCL), can obtain

I _ro=i _d-(g _mV ₁+g _mbV _bs)

=i _d-(g _mV ₁+g _mbV ₁)

=i _d+(g _m+g _mb)i _dRs

Use Kirchhoff's second law, R at output loop _sshould equal V with the pressure drop sum on ro _xso,

V _X=I _ro*ro+i _d*R _S

=[ ⁱ _d+(g _m+g _mb) ⁱ _d ^Rs]*ro+ ⁱ _d* ^R _S

Draw thus circuit output impedance:

$R_{\mathrm{out}}=\frac{\mathrm{Vx}}{i_d}=R_S+\mathrm{ro}+(g_m+g_{\mathrm{mb}})R_S\mathrm{ro}$

When MOS transistor is operated in saturation region, have substitution above formula can obtain

$\mathrm{Av}=\frac{1+(g_m+g_{\mathrm{mb}}+g_{\mathrm{mb}})R_S}{g_{\mathrm{mb}}}$

Can find out, adopt analytical method of the present invention and adopt the method result of calculation of traditional small-signal equivalent circuit figure consistent.And the present invention only need analyze the feedback factor of circuit, adopt the Integrative expression formula that provides of the present invention can obtain fast the small-signal parameters such as the small signal gain of circuit, input impedance, output impedance.And adopt traditional solution, and need draw small-signal equivalent circuit figure, and list a series of equations and solve, its step complexity and computational efficiency are lower.

The present embodiment only provides the gain of MOS transistor common source amplifying circuit small signal, with output impedance method for solving, advantage of the present invention is described as an example.After the same method, method of the present invention can be applied in the analysis and design of analog integrated circuit of various MOS transistor amplifying circuits formations.

Above-described embodiment is preferably execution mode of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be equivalent substitute mode, within being included in protection scope of the present invention.

Claims (2)

1. for a small-signal analysis method for MOS transistor analog integrated circuit, it is characterized in that, comprise the following steps:

(1) extract multiport amplifier model, multiport amplifier model is as follows: by the small-signal drain-source current i in MOS transistor _dbe expressed as amplification coefficient vector with small-signal control voltage vector product, wherein, gm changes the amplification coefficient causing, g by grid voltage _mbthe amplification coefficient being caused by body bias effect, g _mbit is the amplification coefficient being caused by channel-length modulation; v _gsrepresent the added small signal in two ends, MOS transistor grid source, v _bsrepresent the added small signal in MOS transistor lining two ends, source, v _dsrepresent the added small signal in MOS transistor drain-source two ends;

(2) determine multiterminal input signal and feedback factor matrix: disconnect feedback, analyze multiport amplifier input signal, the then impact on multiport amplifier net input signal according to other elements of Signal Analysis System of output, determines feedback factor matrix;

(3) according to multiterminal control reponse system model, solve output signal, wherein said multiterminal control reponse system model is: a Circuits System is equivalent to M input and N output; M input end signal amplifies through multiport amplifier A, and the output signal of N output, through multiple feedback loop F, forms feedback summation signals GS at input, and the stack of feedback summation signals and input signal forms the net input signal D of multiport amplifier A; If M input (I ₁, I ₂..., I _m) formation input signal matrix [I], N output (O ₁, O ₂..., O _n) formation output signal matrix [O]; Output signal matrix [O] is the multiterminal feedback loop of M × N matrix [F] through a feedback factor, forms feedback summation matrix [GS] at M input; This feedback summation matrix [GS] forms net input signal matrix [D] with input signal matrix [I] stack; Amplification coefficient is that multiport amplifier and the multiterminal feedback loop of N × Metzler matrix [A] forms MOS transistor multiterminal small-signal closed-loop system; [E] representation unit matrix, the pass between each multiterminal signal is: [O]=([E]+[A] [F]) ^-1[A] [I];

(4) according to the definition of each small-signal parameter, utilize output signal, solve small-signal parameter.

2. according to the small-signal analysis method for MOS transistor analog integrated circuit described in claims 1, it is characterized in that, voltage gain, output impedance, transfer function, input impedance that described method is applied to the analog integrated circuit that various MOS transistor amplifying circuits are formed solve.