CN102340284A - Low power voltage transconductance adjustable transconductance-constant rail-to-rail input operational amplifier - Google Patents

Abstract

The invention relates to a low-power voltage transconductance adjustable transconductance-constant rail-to-rail input operational amplifier, which comprises a transconductance-constant control circuit, a rail-to-rail input stage and an output stage, wherein the transconductance-constant control circuit makes the transconductance of the rail-to-rail input operational amplifier approximate to twice a reciprocal of a resistance value of a reference resistor by feeding back and controlling the tail current of the rail-to-rail input stage. Simultaneously, the transconductance of the rail-to-rail input operational amplifier can be changed by changing the resistance value of the reference resistor. The rail-to-rail input operational amplifier can work under a low power voltage, and has the advantages of rail-to-rail common mode input range, transconductance adjustability, constant transconductance and the like.

Description

The rail-to-rail input operational amplifier of the constant transconductance that a kind of low supply voltage mutual conductance is adjustable

Technical field

The present invention relates to the operational amplifier technical field, relate in particular to a kind of rail-to-rail input operational amplifier of low supply voltage constant transconductance.

Background technology

Operational amplifier is an important module in the analog integrated circuit.Along with the high speed development of microelectronics manufacture craft technology, the characteristic size of device is more and more littler, and the supply voltage that can bear is also more and more lower, and this can limit the performance of operational amplifier, such as the common-mode input range of operational amplifier.When operational amplifier is used as buffer, need with the same big common-mode input range of input reference signal.At this moment just need to use rail-to-rail input operational amplifier to obtain big dynamic range.

Rail-to-rail input operational amplifier is a kind of amplifier of specific type, and its common-mode input voltage range is to the positive voltage rail from the negative supply voltage rail.Its input stage is imported importing forming with a pair of nmos differential by a pair of PMOS difference.When input common mode voltage near the negative supply voltage rail, the PMOS difference is imported conducting, nmos differential is imported ending; When input common mode voltage near the positive voltage rail, the PMOS difference is imported ending, nmos differential is imported conducting; In the time of in the middle of input common mode voltage is in positive voltage and negative supply voltage, the input of PMOS difference is to importing all conductings with nmos differential.The problem that rail-to-rail input operational amplifier exists is that its mutual conductance meeting has greatly changed along with the variation of input common mode voltage (in some cases, its mutual conductance changes can reach 100%), and this might make circuit vibrate.Mutual conductance feedback is one of the method that is used to realize the rail-to-rail input operational amplifier of constant transconductance at present.Existing mutual conductance feedback method all is to adopt a difference input to being used as with reference to mutual conductance; Through the nmos differential in the input stage being imported to importing duplicating the mutual conductance that obtains input stage with the PMOS difference; Through feedback the two is equated, thereby make the mutual conductance of input stage constant.But in existing circuit implementation method; Because the input of the nmos differential of input stage is to importing having different input common mode voltage (the former is rail-to-rail input common mode voltage, and the latter is a fixing input common mode voltage) with the nmos differential that duplicates, this makes the two when input common mode voltage is low; Its mutual conductance has bigger difference; Also require work under higher supply voltage simultaneously, (such as under the working power voltage of 3V, its mutual conductance fluctuation is about 3～4% otherwise can cause the interior mutual conductance of whole common-mode input range to have bigger fluctuation; And when 1V, its mutual conductance fluctuation is about 11%).

Summary of the invention

Main purpose of the present invention is to overcome the deficiency of prior art, and the rail-to-rail input operational amplifier of the adjustable constant transconductance of a kind of low supply voltage mutual conductance is provided.

In order to achieve the above object, technical scheme of the present invention is: the rail-to-rail input operational amplifier (as shown in Figure 1) of the constant transconductance that a kind of low supply voltage mutual conductance is adjustable, form by constant transconductance control circuit (1), rail-to-rail input stage (2) and output stage (3);

The Vinp input of said constant transconductance control circuit (1) links to each other with Vinn with the analog input signal Vinp of outside respectively with the Vinn input; Its V _BnOutput and V _BpOutput respectively with the V of said rail-to-rail input stage (2) _BnInput and V _BpInput links to each other;

The Vinp input of said rail-to-rail input stage (2) links to each other with Vinn with the analog input signal Vinp of outside respectively with the Vinn input; Its pOp, pOn, four outputs of nOp and nOn link to each other with I_pinp, I_pinn, four inputs of I_ninp and I_ninn of said output stage (3) respectively;

The output result of the vout output output amplifier of said output stage (3).

Among the present invention, constant transconductance control circuit (as shown in Figure 2) is by biasing circuit (1.1), and current operator circuit (1.2) and mutual conductance feedback circuit (1.3) are formed; Be used for producing output signal V _BpAnd V _Bn, control respectively in the rail-to-rail input stage (2) nmos differential input to the right tail current of PMOS difference input, make the mutual conductance of rail-to-rail input stage (2) be approximately 2 times of inverse of reference resistance resistance.Wherein:

Said biasing circuit (1.1) has 2 outputs, and being used for provides bias voltage V to the metal-oxide-semiconductor of mutual conductance feedback circuit (1.3) _B3With reference voltage DeltaV; V _B3NMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₁₈With NMOS pipe M ₁₉Grid link to each other; PMOS pipe M in DeltaV output and the mutual conductance feedback circuit (1.3) ₇With PMOS pipe M ₁₇Grid link to each other.

Current operator circuit (1.2) has four outputs, and being used for provides bias voltage to the metal-oxide-semiconductor of mutual conductance feedback circuit (1.3); V _B4PMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₈Grid link to each other; V _B5NMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₁₃Grid link to each other; V _B6PMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₁Grid link to each other; V _B7NMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₂Grid link to each other; Its function is to make NMOS pipe M ₁₃With PMOS pipe M ₁Nmos differential input in the electric current that flows through and the rail-to-rail input stage (2) becomes certain proportionate relationship to the tail current that flows through, and makes NMOS pipe M ₂With PMOS pipe M ₈PMOS difference input in the electric current that flows through and the rail-to-rail input stage (2) becomes certain proportionate relationship to the tail current that flows through.

Mutual conductance feedback circuit (1.3) is made up of 23 metal-oxide-semiconductors and 5 current sources; PMOS manages M ₁Drain electrode and current source I ₁An end, NMOS manage M ₂Drain electrode, NMOS manage M ₃Drain and gate, NMOS manage M ₅The grid concurrent; NMOS manages M ₅Drain electrode and PMOS pipe M ₄Drain and gate, PMOS manage M ₆Grid, PMOS manage M ₁₄The grid concurrent; PMOS manages M ₆Drain electrode and PMOS pipe M ₇Source electrode, PMOS manage M ₁₁Drain and gate, NMOS manage M ₉The drain and gate concurrent; PMOS manages M ₁₄Drain electrode and PMOS pipe M ₁₅Source electrode, PMOS manage M ₁₂Drain and gate, NMOS manage M ₁₀The drain and gate concurrent; PMOS manages M ₈Drain electrode and PMOS pipe M ₁₁Source electrode, PMOS manage M ₁₂The source electrode concurrent; NMOS manages M ₁₃Drain electrode and NMOS pipe M ₉Source electrode, NMOS manage M ₁₀The source electrode concurrent; PMOS manages M ₇Drain electrode and PMOS pipe M ₁₆Drain electrode, NMOS manage M ₂₀Drain electrode, NMOS manage M ₁₈The source electrode concurrent; PMOS manages M ₁₅Drain electrode and PMOS pipe M ₁₇Drain electrode, NMOS manage M ₂₁Drain electrode, NMOS manage M ₁₉The source electrode concurrent; PMOS manages M ₁₅Grid and PMOS pipe M ₁₆The grid concurrent, and link to each other with ground GND; PMOS manages M ₁₆Source electrode and reference resistance R ₁An end, current source I ₂An end concurrent; PMOS manages M ₁₇Source electrode and reference resistance R ₁The other end, current source I ₃An end concurrent; NMOS manages M ₁₈Drain electrode and NMOS pipe M ₂₀Grid, NMOS manage M ₂₁Grid, current source I ₄An end concurrent; NMOS manages M ₁₉Drain electrode and PMOS pipe M ₂₂Grid, current source I ₅An end concurrent, and with said output V _BpLink to each other; PMOS manages M ₂₂Drain electrode and NMOS pipe M ₂₃Grid with the drain electrode concurrent and with said output V _BnLink to each other; PMOS manages M ₁Source electrode, PMOS manage M ₄Source electrode, PMOS manage M ₆Source electrode, PMOS manage M ₁₄Source electrode, PMOS manage M ₂₂Source electrode, current source I ₁The other end, current source I ₂The other end, current source I ₃The other end, current source I ₄The other end, current source I ₅Other end concurrent and with supply voltage V _DDLink to each other; NMOS manages M ₂Source electrode, NMOS manage M ₃Source electrode, NMOS manage M ₅Source electrode, NMOS manage M ₂₀Source electrode, NMOS manage M ₂₁Source electrode, NMOS manage M ₂₃The source electrode concurrent and link to each other with ground GND.

Among the present invention, when the input common mode voltage of rail-to-rail input operational amplifier changed, said constant transconductance control circuit (1) was through feedback, and the nmos differential input of adjusting rail-to-rail input stage (2) makes NMOS pipe M to importing right tail current with the PMOS difference ₉With PMOS pipe M ₁₁The inverse of mutual conductance sum approximate with reference resistance R ₁The half the of resistance equate.And NMOS pipe M ₉With NMOS pipe M ₁₀, PMOS manages M ₁₁With PMOS pipe M ₁₂Be respectively that nmos differential is imported to importing right duplicating with the PMOS difference, so NMOS pipe M in the rail-to-rail input stage (2) ₉With PMOS pipe M ₁₁The mutual conductance sum equate with the mutual conductance of rail-to-rail input stage (2), thereby make rail-to-rail input operational amplifier have the characteristic of constant transconductance.Simultaneously, change reference resistance R ₁Resistance, can change the mutual conductance of rail-to-rail input operational amplifier, thereby realize the adjustable function of mutual conductance.

The rail-to-rail input operational amplifier of the constant transconductance that low supply voltage mutual conductance of the present invention is adjustable has following beneficial effect:

1, the rail-to-rail input operational amplifier that utilizes the present invention to realize, when supply voltage was 1V, when 0 changed to 1V, its mutual conductance fluctuation can be about 1.2% at common mode input.Therefore the present invention can reach reasonable compromise in power consumption and aspect of performance when being used to realize the rail-to-rail input operational amplifier of constant transconductance under the low supply voltage.

2, utilize the present invention, can change the mutual conductance of rail-to-rail input operational amplifier through the resistance of reference resistance in the adjustment circuit, thereby realize that its mutual conductance is adjustable.

Description of drawings

Fig. 1 is the system assumption diagram of the rail-to-rail input operational amplifier of the adjustable constant transconductance of low supply voltage mutual conductance of the present invention

Fig. 2 is the circuit diagram of constant transconductance control circuit of the present invention

Embodiment

Below in conjunction with accompanying drawing to further explain of the present invention.

Shown in Figure 1 is the system assumption diagram of the rail-to-rail input operational amplifier of the adjustable constant transconductance of low supply voltage mutual conductance provided by the invention, comprises constant transconductance control circuit (1), rail-to-rail input stage (2) and output stage (3).

Fig. 2 is the circuit diagram of constant transconductance control circuit of the present invention.

Biasing circuit (1.1) is used for producing common bank tube M ₁₈And M ₁₉Bias voltage.Current source I ₄With current source I ₅As by M ₁₈, M ₁₉, M ₂₀And M ₂₁The active load of the trans-impedance amplifier of forming.

Current operator circuit (1.2) is used for producing metal-oxide-semiconductor M ₁, M ₂, M ₈And M ₁₃Bias voltage, make and flow through M ₁, M ₂, M ₈And M ₁₃Electric current satisfy formula (1):

$I_{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="HSA00000204042700011.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}=0.5*K_1{I}_n,$ $I_{{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HSA00000204042700011.png"\; state="\{\{state\}\}">M</figure-callout>}}_2}=0.5*K_1{I}_p,$ $I_{M_8}=I_p,$ $I_{M_{13}}=I_n---\left(1\right)$

I in the formula (1) _nAnd I _pBe respectively the tail current of the NMOS pipe in the rail-to-rail input stage (2) and the tail current of PMOS pipe, K ₁Be scale factor, its value can equal 1, also can be less than 1.

If current source I ₂And I ₃The electric current that flows through is I, then current source I ₁Electric current be:

$I_{{\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="HSA00000204042700011.png"\; state="\{\{state\}\}">I</figure-callout>}}_1}=K_{1}I---\left(2\right)$

M ₄Pipe, M ₆Pipe and M ₁₄The ratio of the breadth length ratio of pipe is: 1: 1/K ₁: 1/K ₁Like this, flow through M ₄, M ₆Pipe and M ₁₄The electric current of pipe is respectively:

$I_{M_4}=K_1(I-0.5I_p+0.5I_n),$ $I_{M_6}=(I-0.5I_p+0.5I_n),$ $I_{M_{14}}=(I-0.5I_p+0.5I_n)---\left(3\right)$

M ₉And M ₁₀Pipe has identical breadth length ratio, and the electric current that flows through them is respectively 0.5I _nM ₁₁And M ₁₂Pipe has identical breadth length ratio, and the electric current that flows through them is respectively 0.5I _pM ₇Pipe, M ₁₅Pipe, M ₁₆And M ₁₇Pipe has identical breadth length ratio.Can know according to KCL theorem and formula (1), flow through M ₇Pipe, M ₁₅Pipe, M ₁₆Pipe and M ₁₇The electric current of pipe is (when difference is input as zero):

$I_{M_7}=I_{M_{15}}=I$ $I_{M_{16}}=I_{M_{17}}=I---\left(4\right)$

M ₇Pipe, M ₁₅Pipe, M ₆Pipe, M ₁₄Pipe, M ₈Pipe, M ₉Pipe, M ₁₀Pipe, M ₁₃Pipe, M ₁₁Pipe and M ₁₂Pipe constitutes a trsanscondutance amplifier, and establishing its mutual conductance is Gm1; M ₁₆Pipe, M ₁₇Pipe, R ₁, I ₂And I ₃Another trsanscondutance amplifier that constitutes, establishing its mutual conductance is Gm2.Input at these two trsanscondutance amplifiers adds an identical little differential voltage (DeltaV-0) (wherein DeltaV is produced by biasing circuit (1.1)) respectively, and the current change quantity that they is produced separately through negative feedback is equal, that is: Δ i ₁=Gm1*DeltaV=Δ i ₂=Gm2*DeltaV, thus make these two trsanscondutance amplifiers have identical mutual conductance, i.e. Gm1=Gm2.

Assuming:

Gm1 and Gm2 are the formula (5) and (6) as follows:

$\mathrm{<figure-callout\; id="1"\; label="Gm"\; filenames="HSA00000204042700011.png"\; state="\{\{state\}\}">Gm</figure-callout>}1=\mathrm{gm}/(2+\frac{2}{\mathrm{gmn}+\mathrm{gmp}+\mathrm{gdsn}+\mathrm{gdsp}}\mathrm{gm})---\left(5\right)$

Gm2＝gm/(2+R ₁gm) (6)

Can get by formula (5) and formula (6):

$R_1=\frac{2}{\mathrm{gmn}+\mathrm{gmp}+\mathrm{gdsn}+\mathrm{gdsp}}---\left(7\right)$

Because gdsn, gdsp is usually much smaller than gmn, gmp, and formula (7) can be write as:

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000204042700011.png"\; state="\{\{state\}\}">R</figure-callout>}}_1\&ap;\frac{2}{\mathrm{gmn}+\mathrm{gmp}}---\left(8\right)$

Because M ₉Pipe and M ₁₀Pipe and the nmos differential in the rail-to-rail input stage (2) are imported identical and have identical tail current, a M ₁₁Pipe and M ₁₂Pipe and the PMOS difference in the rail-to-rail input stage (2) are imported identical and have identical tail current, and the mutual conductance gm_opa of rail-to-rail input stage is:

gm_opa＝gmn+gmp (9)

Can know by formula (8) and formula (9): the mutual conductance of rail-to-rail input stage, i.e. the mutual conductance of rail-to-rail input operational amplifier is:

gm_opa≈2/R ₁ (10)

Can know that by formula (10) mutual conductance of rail-to-rail input stage is approximately reference resistance R ₁2 times of inverse, if change reference resistance R ₁Value, just can change the mutual conductance of rail-to-rail input stage.

The rail-to-rail input operational amplifier of the constant transconductance that low supply voltage mutual conductance provided by the invention is adjustable has the advantage that working power voltage is low, the mutual conductance fluctuation is little.Simulation result shows, when supply voltage was 1V, when 0 changed to 1V, its mutual conductance fluctuation can be about 1.2% at common mode input.And can change the mutual conductance of rail-to-rail input operational amplifier through the resistance of reference resistance in the adjustment circuit, thereby realize that its mutual conductance is adjustable.

Claims (6)

1. the rail-to-rail input operational amplifier of the adjustable constant transconductance of a low supply voltage mutual conductance is characterized in that: be made up of constant transconductance control circuit (1), rail-to-rail input stage (2) and output stage (3);

The Vinp input of said constant transconductance control circuit (1) links to each other with Vinn with the analog input signal Vinp of outside respectively with the Vinn input; Its V _BnOutput and V _BpOutput respectively with the V of said rail-to-rail input stage (2) _BnInput and V _BpInput links to each other;

The Vinp input of said rail-to-rail input stage (2) links to each other with Vinn with the analog input signal Vinp of outside respectively with the Vinn input; Its pOp, pOn, four outputs of nOp and nOn link to each other with I_pinp, I_pinn, four inputs of I_ninp and I_ninn of said output stage (3) respectively;

The output result of the vout output output amplifier of said output stage (3).

2. the rail-to-rail input operational amplifier of the constant transconductance that low supply voltage mutual conductance according to claim 1 is adjustable; It is characterized in that: said constant transconductance control circuit (1) is by biasing circuit (1.1), and current operator circuit (1.2) and mutual conductance feedback circuit (1.3) are formed; Be used for producing output signal V _BpAnd V _Bn, control respectively in the rail-to-rail input stage (2) nmos differential input to the right tail current of PMOS difference input, make the mutual conductance of rail-to-rail input stage (2) be approximately 2 times of inverse of reference resistance resistance.

3. the rail-to-rail input operational amplifier of the constant transconductance that low supply voltage mutual conductance according to claim 2 is adjustable is characterized in that: said biasing circuit (1.1) has 2 outputs, and being used for provides bias voltage V to the metal-oxide-semiconductor of mutual conductance feedback circuit (1.3) _B3With reference voltage DeltaV; V _B3NMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₁₈With NMOS pipe M ₁₉Grid link to each other; PMOS pipe M in DeltaV output and the mutual conductance feedback circuit (1.3) ₇With PMOS pipe M ₁₇Grid link to each other.

4. the rail-to-rail input operational amplifier of the constant transconductance that low supply voltage mutual conductance according to claim 2 is adjustable; It is characterized in that: described current operator circuit (1.2) has four outputs, and being used for provides bias voltage to the metal-oxide-semiconductor of mutual conductance feedback circuit (1.3); V _B4PMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₈Grid link to each other; V _B5NMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₁₃Grid link to each other; V _B6PMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₁Grid link to each other; V _B7NMOS pipe M in output and the mutual conductance feedback circuit (1.3) ₂Grid link to each other; Make NMOS pipe M ₁₃With PMOS pipe M ₁Nmos differential input in the electric current that flows through and the rail-to-rail input stage (2) becomes certain proportionate relationship to the tail current that flows through, and makes NMOS pipe M ₂With PMOS pipe M ₈PMOS difference input in the electric current that flows through and the rail-to-rail input stage (2) becomes certain proportionate relationship to the tail current that flows through.

5. the rail-to-rail input operational amplifier of the constant transconductance that low supply voltage mutual conductance according to claim 2 is adjustable is characterized in that: described mutual conductance feedback circuit (1.3) is made up of 23 metal-oxide-semiconductors and 5 current sources; PMOS manages M ₁Drain electrode and current source I ₁An end, NMOS manage M ₂Drain electrode, NMOS manage M ₃Drain and gate, NMOS manage M ₅The grid concurrent; NMOS manages M ₅Drain electrode and PMOS pipe M ₄Drain and gate, PMOS manage M ₆Grid, PMOS manage M ₁₄The grid concurrent; PMOS manages M ₆Drain electrode and PMOS pipe M ₇Source electrode, PMOS manage M ₁₁Drain and gate, NMOS manage M ₉The drain and gate concurrent; PMOS manages M ₁₄Drain electrode and PMOS pipe M ₁₅Source electrode, PMOS manage M ₁₂Drain and gate, NMOS manage M ₁₀The drain and gate concurrent; PMOS manages M ₈Drain electrode and PMOS pipe M ₁₁Source electrode, PMOS manage M ₁₂The source electrode concurrent; NMOS manages M ₁₃Drain electrode and NMOS pipe M ₉Source electrode, NMOS manage M ₁₀The source electrode concurrent; PMOS manages M ₇Drain electrode and PMOS pipe M ₁₆Drain electrode, NMOS manage M ₂₀Drain electrode, NMOS manage M ₁₈The source electrode concurrent; PMOS manages M ₁₅Drain electrode and PMOS pipe M ₁₇Drain electrode, NMOS manage M ₂₁Drain electrode, NMOS manage M ₁₉The source electrode concurrent; PMOS manages M ₁₅Grid and PMOS pipe M ₁₆The grid concurrent, and link to each other with ground GND; PMOS manages M ₁₆Source electrode and reference resistance R ₁An end, current source I ₂An end concurrent; PMOS manages M ₁₇Source electrode and reference resistance R ₁The other end, current source I ₃An end concurrent; NMOS manages M ₁₈Drain electrode and NMOS pipe M ₂₀Grid, NMOS manage M ₂₁Grid, current source I ₄An end concurrent; NMOS manages M ₁₉Drain electrode and PMOS pipe M ₂₂Grid, current source I ₅An end concurrent, and with said output V _BpLink to each other; PMOS manages M ₂₂Drain electrode and NMOS pipe M ₂₃Grid with the drain electrode concurrent and with said output V _BnLink to each other; PMOS manages M ₁Source electrode, PMOS manage M ₄Source electrode, PMOS manage M ₆Source electrode, PMOS manage M ₁₄Source electrode, PMOS manage M ₂₂Source electrode, current source I ₁The other end, current source I ₂The other end, current source I ₃The other end, current source I ₄The other end, current source I ₅Other end concurrent and with supply voltage V _DDLink to each other; NMOS manages M ₂Source electrode, NMOS manage M ₃Source electrode, NMOS manage M ₅Source electrode, NMOS manage M ₂₀Source electrode, NMOS manage M ₂₁Source electrode, NMOS manage M ₂₃The source electrode concurrent and link to each other with ground GND.

6. according to the rail-to-rail input operational amplifier of the adjustable constant transconductance of the arbitrary described low supply voltage mutual conductance of claim 1-5; It is characterized in that; When the input common mode voltage of rail-to-rail input operational amplifier changes; Said constant transconductance control circuit (1) is through feedback, and the nmos differential input of adjusting rail-to-rail input stage (2) makes NMOS pipe M to importing right tail current with the PMOS difference ₉With PMOS pipe M ₁₁The inverse of mutual conductance sum approximate with reference resistance R ₁The half the of resistance equate; And NMOS pipe M ₉With NMOS pipe M ₁₀, PMOS manages M ₁₁With PMOS pipe M ₁₂Be respectively that the nmos differential input is to importing right duplicating with the PMOS difference in the rail-to-rail input stage (2), NMOS manages M ₉With PMOS pipe M ₁₁The mutual conductance sum equate with the mutual conductance of rail-to-rail input stage (2), make rail-to-rail input operational amplifier have the characteristic of constant transconductance, simultaneously, change reference resistance R ₁Resistance, change the mutual conductance of rail-to-rail input operational amplifier, realize that mutual conductance is adjustable.

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