CN102591395A - Constant current source circuit with band-gap reference function - Google Patents

Abstract

The invention relates to a constant current source circuit with a band-gap reference function, comprising a band-gap reference core unit, a band-gap reference bias unit and a constant current source output unit, wherein the band-gap reference bias unit is used for providing bias current to a band-gap reference core; the band-bap reference core unit is used for providing band-gap reference voltage with a certain temperature coefficient to the constant current source output unit; and by combining a fuse wire trimming structure of the constant current source output unit, current of a whole constant current source branch can be adjusted. Through adjusting the temperature coefficient of the band-gap reference voltage to be matched with a temperature coefficient of resistance of the constant current source output unit, constant current source current which is insensitive to supply voltage and temperature is obtained. The constant current source circuit is applied to linear power supplies with micro power consumption and low voltage difference to ensure that the temperature coefficient of static current of the linear power supplies with low voltage difference is less than 50 ppm/DEG C, and the rejection ratio of the supply voltage is greater than 60 dB. The constant current source circuit can be applied to the field of linear power supplies with micro power consumption and low voltage difference.

Description

Constant-current source circuit with band gap reference function

Technical field

The present invention relates to a kind of constant-current source circuit, particularly a kind of constant-current source circuit with band gap reference function, it directly applies to little pressure reduction linear power supply low in energy consumption field.

Background technology

Constant-current source circuit is the core cell of low pressure difference linearity power supply, and the constant-current source circuit that especially has the band-gap reference performance is applied to little pressure reduction linear power supply low in energy consumption.Fig. 1 is the circuit block diagram of the little pressure reduction linear power supply low in energy consumption of tradition, and it is made up of element circuits such as band gap reference, error amplifier, PMOS adjustment pipe, constant-current source circuit, mistake/under-voltage protection, mistake/undercurrent protections.Constant-current source circuit provides bias current for error amplifier, band gap reference, mistake/under-voltage protection, mistake/undercurrent protection etc.; It is the Key Circuit unit of little pressure reduction linear power supply low in energy consumption; The electric current that constant-current source circuit provides determines the changing value of the quiescent current of little pressure reduction linear power supply low in energy consumption with supply voltage, variation of temperature value; Like the electric current of Widdlar micro-current source with the rate of change of supply voltage greater than 10%, usually greater than 1800ppm/ ℃, do not satisfy the requirement of little pressure reduction linear power supply low in energy consumption with variation of temperature; Therefore, pressed for supply voltage, the insensitive constant-current source circuit of temperature variation.

At present, constant-current source circuit of a great variety has Widdlar micro-current source, the bias current sources of using thermodynamics voltage, high precise current source etc.In these constant-current source circuits, it is big with mains voltage variations that its output current has, and the temperature coefficient that has is bigger, as their temperature coefficient, greater than 1800ppm/ ℃, can not satisfy the requirement of the pressure reduction linear power supply little low in energy consumption that quiescent current is had relatively high expectations.(Zheng Xiao etc., patent name: high-precision constant flow source circuit, the patent No.: the circuit diagram of high precise current source 200910162724.5) is as shown in Figure 2 for document 1.It is through introducing the electric current I of negative temperature coefficient _PTAT, having improved the temperature performance of bias current, its temperature coefficient is 125ppm/ ℃, but the I in its current mirror electric current ₁, I ₂Receive the variation of supply voltage and fluctuate, still can not satisfy the requirement of the pressure reduction linear power supply little low in energy consumption that quiescent current is had relatively high expectations.

Summary of the invention

The present invention provides a kind of constant-current source circuit with band gap reference function, to overcome, the problem that temperature coefficient bigger responsive to mains voltage variations in traditional constant-current source circuit, to satisfy the high performance requirements of little pressure reduction linear power supply low in energy consumption.

The present invention solves the problems of the technologies described above the technical scheme of being taked and is, the constant-current source circuit with band gap reference performance of the present invention contains:

A kind of constant-current source circuit with band gap reference function is characterized in that containing:

A band-gap reference vouching unit provides the constant current source electric current, comprising:

Three NPN pipe Q ₁, Q ₂, Q ₅, three PNP pipe Q ₃, Q ₄, Q ₆, two capacitor C ₁, C ₂, six resistance R ₁, R ₂, R ₃, R ₄, R ₅, R ₁₁Repair tune switch K with three fuses ₁, K ₂, K ₃,

Wherein, the base stage of Q3 and Q ₄Base stage, Q ₃Collector connect Q ₃Emitter and Q ₄Emitter, Q ₆Emitter, C ₁Top crown link together, and join capacitor C with biasing input point A ₁Bottom crown ground connection, Q ₂Collector and Q ₃Collector, Q ₁Collector, Q ₄Collector, Q ₆Base stage, C ₂Top crown connect C ₂Bottom crown ground connection, Q ₆Collector meet R ₁₁A end, R ₁₁B end ground connection, resistance R ₁A termination Q ₂Emitter, R ₁Emitter, the R of b end and Q1 ₂A end connect K ₁A end and R ₃A end, R ₂B end connect K ₁B end and R ₃B end, K ₂A end, R ₄A end connect K ₂B end and R ₄B end, K ₃A end, R ₅A end connect K ₃B termination R ₅B end, and ground connection, Q ₅The M5 drain electrode of collector and constant current source output unit join Q ₅Base stage meet biasing input point A, Q ₅Emitter and Q ₂Base stage, Q ₁Base stage connect, be the output terminal V of band-gap reference _REF

A band-gap reference bias unit provides bias current, comprising:

Four PMOS pipe M ₁, M ₂, M ₃, M ₄, four NPN pipe Q ₇, Q ₈, Q ₉, Q ₁₀And resistance R ₆,

Wherein, the source electrode of M1 and substrate and power supply V _CCJoin, the drain electrode of M1 is biasing input point A, the source electrode of M2 and substrate and power supply V _CCJoin M ₁Grid and M ₂Grid, M ₂Drain electrode, Q ₈Emitter link together M ₄Drain electrode and Q ₇Base stage, Q ₈Base stage, Q ₇Emitter link together Q ₈Emitter and Q ₁₀Collector, Q ₉Base stage link together; Q ₇Emitter and Q ₉Collector, Q ₁₀Base stage connect Q ₉Grounded emitter, Q ₁₀Emitter meet R ₆A end, R ₆B end ground connection, M ₃Source electrode and substrate and power supply V _CCJoin M ₃Grid, drain electrode meet M ₄Source electrode, M ₄Substrate and power supply V _CCJoin M ₄Grounded-grid, M ₄Drain electrode meet Q ₇Collector;

A constant current source output unit, output constant current source electric current comprises:

Four PMOS pipe M ₅, M ₆, M ₇, M ₈, a NPN pipe Q ₅, four resistance R ₇, R ₈, R ₉, R ₁₀Repair tune switch K with three fuses ₄, K ₅, K ₆,

Wherein, M ₅, M ₆, M ₇, M ₈Source electrode and substrate all with power supply V _CCLink together M ₅, M ₆, M ₇, M ₈Grid all and M ₅Drain electrode join, with Q in the band-gap reference vouching unit ₅Collector link together Q ₅Base stage meet biasing input point A, Q ₅Emitter and R ₇A end join M ₆Drain electrode output constant current source electric current I ₁, M ₇Drain electrode output constant current source electric current I ₂, M ₈Drain electrode output constant current source electric current I ₃, K ₄A end, resistance R ₈A end, resistance R ₇B end link together K ₄B end and R ₈B end, K ₅A end, R ₉A end connect K ₅B end and R ₉B end, K ₆A end, R ₁₀A end connect K ₆B end and R ₁₀B end join.

Beneficial effect:

Constant-current source circuit with band-gap reference function of the present invention is compared with traditional constant-current source circuit, and it has following characteristics:

1. in the band-gap reference bias unit of circuit of the present invention, through regulating NPN pipe Q ₉, Q ₁₀Emitter area ratio and R ₆Resistance value is confirmed PMOS pipe M ₂Electric current, through M ₁, M ₂The image current mirror, make its electric current that provides and independent of power voltage, and it is very little influenced by variation of temperature.Therefore, circuit of the present invention can provide supply voltage and all insensitive bias current of temperature.

2. the band gap base vouching of circuit of the present invention unit is the resistance R of constant current source output unit ₇Reference voltage V is provided _REF, by the definite electric current I of band gap base vouching unit ₀=V _REF/ R ₇, it and independent of power voltage are through making V _REFTemperature coefficient and resistance R ₇Temperature coefficient be complementary, then can obtain temperature-resistant constant current source electric current I ₀, the constant current source output current I that penetrates through the image current mirroring ₁, I ₂, I ₃Has I ₀Same performance.

Therefore; When the input voltage of the constant current source electric current of circuit of the present invention changes at 2.7V～6V; The rejection ratio that electric current changes is 60dB, and in-55 ℃～125 ℃ temperature, the temperature coefficient of its quiescent current is less than 50ppm/ ℃; Temperature coefficient than document 1 reduces more than one times, can satisfy the high performance requirements of little pressure reduction linear power supply low in energy consumption.

Description of drawings

Fig. 1 is the circuit block diagram of the constant-current source circuit of the little pressure reduction low in energy consumption of tradition;

Fig. 2 is the circuit block diagram of the high-precision constant flow source circuit of document 1;

Fig. 3 is the circuit diagram with constant-current source circuit of band-gap reference function of the present invention.

Embodiment

Embodiment of the present invention is not limited only to following description, combines accompanying drawing to further specify at present.

The circuit diagram of the constant-current source circuit with band-gap reference function of the present invention is as shown in Figure 3, and circuit of the present invention is made up of band-gap reference vouching unit, band-gap reference bias unit and constant current source output unit.Wherein, The band-gap reference bias unit is that band-gap reference vouching unit provides bias current; Band-gap reference vouching unit provides reference voltage for the constant current source output unit, and the constant current source output unit is repaiied tune switch adjustment constant current source electric current through fuse, reaches the purpose of control entire circuit quiescent current.

In band-gap reference vouching unit, Q ₁, Q ₂Collector respectively as the end of oppisite phase and the in-phase end of error amplifier, through Q ₄, Q ₆Path, control Q ₅The emitter output voltage V _REF, Q ₁, Q ₂Area than definite resistance R ₁The voltage at two ends is confirmed the electric current that the band-gap reference vouching is first, can confirm resistance R ₂On voltage drop, in conjunction with Q ₁Forward voltage drop V _BE, can get Q ₅The emitter output voltage V _REFValue.Select K ₁, K ₂, K ₃Break-make and R ₃, R ₄, R ₅Choosing of value can be adjusted the value of band-gap reference.Q ₅Be the efferent duct of band-gap reference, make band-gap reference have certain electric current fan-out capability.Select R ₁, R ₂Resistance, in conjunction with Q ₁, Q ₂Forward voltage drop, just can obtain the bandgap voltage reference V of uniform temperature coefficient _REF

In the band-gap reference bias unit, by M ₁, M ₂, M ₃, M ₄, Q ₇, Q ₈, Q ₉, Q ₁₀, R ₆Constitute bias unit, M ₁, M ₂Be current mirror, M ₁Examine the input point A that promptly setovers for band gap reference bias current is provided, and Q ₇, Q ₈, Q ₉, Q ₁₀, R ₆Confirm the bias unit bias current, Q ₉, Q ₁₀Area is than definite resistance R ₆The voltage drop at two ends is in conjunction with R ₆The resistance of resistance promptly confirm M ₂The bias current of branch road, M ₁The bias current of biasing branch road is by M ₁With M ₂The pipe sizing relation is confirmed.Q ₇, Q ₈Base stage connect together the knot Q ₇Collector, M ₃, M ₄Be Q ₇, Q ₈Bias current is provided.

In the constant current source output unit, M ₅, M ₆, M ₇, M ₈Constitute the image current mirror, M ₅, Q ₅, R ₇, R ₈, R ₉, R ₁₀And fuse-switch K ₄, K ₅, K ₆Constitute the master control current branch of constant current source output unit, Q ₅The emitter output voltage be V _REFAnd resistance R ₇Confirm the electric current I of constant current source master control branch road ₀, rationally adjust the band-gap reference output voltage V _REFTemperature performance combine resistance R ₇Temperature coefficient, can obtain the very little constant current source electric current I of temperature coefficient ₀, through M ₆, M ₇, M ₈, M ₅The image current mirror, just can be with I ₀Be mirrored to I ₁, I ₂, I ₃, designed resistance R ₈, R ₉, R ₁₀And fuse-switch K ₄, K ₅, K ₆To I ₀Value adjust, work as I like this ₀When changing, I ₀Image current I ₁, I ₂, I ₃Change simultaneously, thereby reach the purpose of controlling the entire circuit quiescent current variation.

The concrete structure of circuit of the present invention and annexation, interactively are identical with the summary of the invention part of this instructions, no longer repeat here.Its principle of work is following:

In the band-gap reference bias unit, establish Q ₁₀, Q ₉The emitter area ratio is 4, R ₆The voltage at two ends is: V _X=V _TLn4 then flows through resistance R ₆Electric current be: I ₆=V _TLn4/R.Current mirror M ₁For band-gap reference provides working current, according to M ₂Electric current and M ₁, M ₂Size can confirm M ₁Electric current.In the circuit of the present invention, M ₁Channel width is M ₂3 times of channel width.

In the band-gap reference vouching unit, Q ₂Emitter area is made as Q ₁8 times, R ₁The voltage at two ends is Q ₁, Q ₂Base-emitter voltage poor, R ₂Temperature coefficient for just, and Q ₁The temperature coefficient of EB junction voltage for negative, the output voltage that then can get the Q5 emitter is V _REF

R ₁The voltage at two ends is: V _X=V _TLn8 flows through Q ₁, Q ₂Collector current be: I ₁=V _TLn8/R ₁, wherein, V _TBe temperature-sensitive voltage: V _T=kt/q=26mV;

Q then ₅The emitter output voltage V _REFFor: $V_{\mathrm{REF}}=V_{\mathrm{EB}}+2\×\frac{V_T\mathrm{Ln}8}{R_1}\×R_2---\left(1\right)$

Q ₁V _BEVoltage:

V _BE(T)＝V _BE0+α(T ₀-T) (2)

(2) in the formula, V _BE0For EB ties in temperature T ₀The time junction voltage, α is the temperature coefficient of triode.

In band-gap reference vouching unit, resistance R ₁, R ₂Adopt polysilicon resistance, its temperature coefficient is R _TC, common R _TCAt 1000ppm/ ℃～2000ppm/ ℃, be positive temperature coefficient (PTC), when temperature raise, resistance increased, otherwise then reduces.When temperature is T, resistance R ₂On voltage reduce to:

R ₂(T)＝R ₂×[1+R _TC×(T-T ₀)] (3)

R ₂Be resistance R ₂In temperature is T ₀Resistance value, in conjunction with (1), (2), (3) formula, then (1) formula is:

$V_{\mathrm{REF}}\left(T\right)=V_{\mathrm{BE}0}+\mathrm{\&alpha;}(T_0-T)+2\&times;\frac{V_T\ln 8}{R_1}\&times;{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000140993000000012.png"\; state="\{\{state\}\}">R</figure-callout>}}_2\&times;[1+R_{\mathrm{TC}}\&times;(T-T_0)]---\left(4\right)$

Resistance R then ₇The voltage at two ends is V _REF, flow through resistance R ₇Electric current be constant current source master control branch current I (T),

$I\left(T\right)=\frac{V_{\mathrm{BE}0}+\mathrm{\&alpha;}(T_0-T)+2\frac{\mathrm{kt}}{q}\&times;\frac{R_2[1+R_{\mathrm{TC}}\&times;(T-T_0)]}{R_1}\&times;\ln N}{R_7[1+R_{\mathrm{TC}}\&times;(T-T_0)]}---\left(5\right)$

This is a function relevant with temperature, order

T-T ₀=T,

Then (5) formula can be reduced to:

$I\left(T\right)=\frac{V_{\mathrm{BE}0}-\mathrm{\&alpha;T}+\mathrm{\&beta;}\frac{R_2}{R_1}+\mathrm{\&beta;}\frac{R_2}{R_1}{R}_{\mathrm{TC}}T}{R_7(R_{\mathrm{TC}}T+1)}---\left(6\right)$

Through (6) formula, to the differentiate of temperature:

$\frac{\&PartialD;I}{\&PartialD;T}=\frac{-\mathrm{\&alpha;}(R_7{R}_{\mathrm{TC}}T+R_7)-R_7{R}_{\mathrm{TC}}[(\mathrm{\&beta;}\frac{R_2}{R_1}{R}_{\mathrm{TC}}-\mathrm{\&alpha;})T+V_{\mathrm{BE}0}+\mathrm{\&beta;}\frac{R_2}{R_1})]}{{(R_7{R}_{\mathrm{TC}}T+R_7)}^2}---\left(7\right)$

(7) formula shows: electric current is a function with variation of temperature, and the extreme value of function is the temperature variant extreme value of electric current, make (7) as shown in the formula:

$f=\frac{-\mathrm{\&alpha;}(R_{\mathrm{TC}}T+1)-R_{\mathrm{TC}}[(\mathrm{\&beta;}\frac{R_2}{R_1}{R}_{\mathrm{TC}}-\mathrm{\&alpha;})T+V_{\mathrm{BE}0}+\mathrm{\&beta;}\frac{R_2}{R_1})]}{R_7{(R_{\mathrm{TC}}T+1)}^2}---\left(8\right)$

Arrangement (8) formula can get:

${\mathrm{fR}}_7{R_{\mathrm{TC}}}^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000140993000000012.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+(2{\mathrm{fR}}_7{R}_{\mathrm{TC}}+{R_{\mathrm{<figure-callout\; id="2"\; label="TC"\; filenames="HDA0000140993000000012.png"\; state="\{\{state\}\}">TC</figure-callout>}}}^2\mathrm{\&beta;}\frac{R_2}{R_1})T+{\mathrm{fR}}_7+\mathrm{\&alpha;}+R_{\mathrm{TC}}{V}_{\mathrm{BE}0}+R_{\mathrm{TC}}\mathrm{\&beta;}\frac{R_2}{R_1}=0---\left(9\right)$

This is a second order function, because the coefficient fR of quadratic function ₇R _TC ²>=0, the curve opening makes progress, so electric current I ₀With temperature variation minimal value is arranged, this extreme value and α, R _TC, R ₁, R ₂, R ₇Relevant.Because of electric current I ₁, I ₂, I ₃With electric current I ₀So mirror image is electric current I ₁, I ₂, I ₃Temperature variant minimal value is arranged.

The basic parameter of circuit of the present invention is:

The threshold voltage V of NMOS pipe _TN: 0.85V～1.05V, source-drain voltage V _DS>=5.5V;

The threshold voltage V of PMOS pipe _TP:-0.83V～-1.03V, source-drain voltage V _DS>=5.5V;

Gate oxide thickness 11.5nm～the 13.5nm of PMOS, NMOS pipe;

The V of NPN pipe _BEFor: 730mV～770mV, BV _CEO>=5.5V;

The V of PNP pipe _BEFor: 625mV～665mV, BV _CEO>=5.5V.

Wherein, in the NPN pipe:

Q ₁, Q ₅, Q ₈, Q ₉Be the pipe of minimum emitter area, its emitter area is 1 μ m * 0.6 μ m, and its emitter area factor is 1; Q ₂Emitter area factor: 8; Q ₇, Q ₁₀Emitter area factor: 4.

In the PNP pipe:

Q ₆Emitter area factor: 1; Q ₄Emitter area factor: 2; Q ₃Emitter area factor: 4.

In the PMOS pipe:

M ₁Size: W/L=48 μ m/26 μ m; M ₂Size: W/L=16 μ m/26 μ m;

M ₃Size: W/L=5 μ m/230 μ m; M ₄Size: W/L=2.4 μ m/3 μ m;

M ₅Size: W/L=20 μ m/12 μ m; M ₆Size: W/L=10 μ m/12 μ m;

M ₇Size: W/L=20 μ m/12 μ m; M ₈Size: W/L=40 μ m/12 μ m.

In the polysilicon resistance:

R ₁：18kΩ～22kΩ；R ₂：86kΩ～94kΩ；R ₃：12.17kΩ～13.17kΩ；

R ₄：6kΩ～6.6kΩ；R ₅：3kΩ～3.34kΩ；R ₆：27kΩ～30.6kΩ；

R ₇：855kΩ～945kΩ；R ₈：460kΩ～500kΩ；R ₉：230kΩ～250kΩ；

R ₁₀：115kΩ～125kΩ；R ₁₁：345kΩ～375kΩ。

Employing is based on the constant-current source circuit with band-gap reference function of above parameter designing; Be applied in little pressure reduction linear power supply low in energy consumption; Can control the variable quantity of the quiescent current of little pressure reduction linear power supply low in energy consumption well with temperature and voltage; Make the low pressure difference linearity power supply under-55 ℃～125 ℃, the temperature coefficient of its quiescent current is less than 50ppm/ ℃, when supply voltage changes at 2.7V～6V; The rejection ratio of quiescent current variation is greater than 60dB, and the quiescent current that can satisfy little pressure reduction linear power supply low in energy consumption is with temperature, requirement that mains voltage variations is little.

Manufacturing process of the present invention is 0.6 μ m BiCMOS technology.

Claims (1)

1. constant-current source circuit with band gap reference function is characterized in that containing:

A band-gap reference vouching unit provides the constant current source electric current, comprising:

Three NPN pipe Q ₁, Q ₂, Q ₅, three PNP pipe Q ₃, Q ₄, Q ₆, two capacitor C ₁, C ₂, six resistance R ₁, R ₂, R ₃, R ₄, R ₅, R ₁₁Repair tune switch K with three fuses ₁, K ₂, K ₃,

Wherein, the base stage of Q3 and Q ₄Base stage, Q ₃Collector connect Q ₃Emitter and Q ₄Emitter, Q ₆Emitter, C ₁Top crown link together, and join capacitor C with biasing input point A ₁Bottom crown ground connection, Q ₂Collector and Q ₃Collector, Q ₁Collector, Q ₄Collector, Q ₆Base stage, C ₂Top crown connect C ₂Bottom crown ground connection, Q ₆Collector meet R ₁₁A end, R ₁₁B end ground connection, resistance R ₁A termination Q ₂Emitter, R ₁Emitter, the R of b end and Q1 ₂A end connect K ₁A end and R ₃A end, R ₂B end connect K ₁B end and R ₃B end, K ₂A end, R ₄A end connect K ₂B end and R ₄B end, K ₃A end, R ₅A end connect K ₃B termination R ₅B end, and ground connection, Q ₅The M5 drain electrode of collector and constant current source output unit join Q ₅Base stage meet biasing input point A, Q ₅Emitter and Q ₂Base stage, Q ₁Base stage connect, be the output terminal V of band-gap reference _REF

A band-gap reference bias unit provides bias current, comprising:

Four PMOS pipe M ₁, M ₂, M ₃, M ₄, four NPN pipe Q ₇, Q ₈, Q ₉, Q ₁₀And resistance R ₆,

Wherein, the source electrode of M1 and substrate and power supply V _CCJoin, the drain electrode of M1 is biasing input point A, the source electrode of M2 and substrate and power supply V _CCJoin M ₁Grid and M ₂Grid, M ₂Drain electrode, Q ₈Emitter link together M ₄Drain electrode and Q ₇Base stage, Q ₈Base stage, Q ₇Emitter link together Q ₈Emitter and Q ₁₀Collector, Q ₉Base stage link together; Q ₇Emitter and Q ₉Collector, Q ₁₀Base stage connect Q ₉Grounded emitter, Q ₁₀Emitter meet R ₆A end, R ₆B end ground connection, M ₃Source electrode and substrate and power supply V _CCJoin M ₃Grid, drain electrode meet M ₄Source electrode, M ₄Substrate and power supply V _CCJoin M ₄Grounded-grid, M ₄Drain electrode meet Q ₇Collector;

A constant current source output unit, output constant current source electric current comprises:

Four PMOS pipe M ₅, M ₆, M ₇, M ₈, a NPN pipe Q ₅, four resistance R ₇, R ₈, R ₉, R ₁₀Repair tune switch K with three fuses ₄, K ₅, K ₆,

Wherein, M ₅, M ₆, M ₇, M ₈Source electrode and substrate all with power supply V _CCLink together M ₅, M ₆, M ₇, M ₈Grid all and M ₅Drain electrode join, with Q in the band-gap reference vouching unit ₅Collector link together Q ₅Base stage meet biasing input point A, Q ₅Emitter and R ₇A end join M ₆Drain electrode output constant current source electric current I ₁, M ₇Drain electrode output constant current source electric current I ₂, M ₈Drain electrode output constant current source electric current I ₃, K ₄A end, resistance R ₈A end, resistance R ₇B end link together K ₄B end and R ₈B end, K ₅A end, R ₉A end connect K ₅B end and R ₉B end, K ₆A end, R ₁₀A end connect K ₆B end and R ₁₀B end join.

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