[Note: analog MOS integrated circuit] bandgap reference (basic principle + current mode + voltage mode circuit explanation)

    In analog circuits , It includes voltage reference and current reference , And the circuit gain 、 Parameters such as output noise and power consumption are often directly related to the benchmark . This reference is usually direct flow , Reference and power supply required 、 Process parameters and temperature are independent （PVT）. The bandgap reference to be discussed below , Its main function is to establish a reference source independent of temperature .

   The purpose of generating a reference is to establish a reference independent of power supply voltage and process 、 DC voltage or current with definite temperature characteristics .

One 、 Generation of zero temperature coefficient

   In analog circuits , Most process parameters change with temperature , A zero temperature coefficient reference usually passes through two different temperature coefficients (TC) The quantities of are added with appropriate weights to obtain . It can be expressed mathematically as follows

  Therefore, we must determine two kinds of voltage with positive temperature coefficient and negative temperature coefficient , in application , Bipolar transistors are commonly used （BJT） To realize the generation of positive and negative temperature coefficients .

Negative temperature coefficient voltage （CTAT)

   For a bipolar device , Its base - Of emitter voltage V_BE Inversely proportional to the absolute temperature （CTAT）, according to PN Junction current formula , You can write ：

   among $V_T=kT/q$ , $b$ Is the scale factor ,$m\approx -1.5$
   obtain $V_{BE}=V_{T}ln(I_S/I_S)$, Easy to know I_C and I_S It's all temperature T Function of , Yes V_BE About T Derivation , obtain

   When ${\mathbf{V}}_{\mathbf{B}\mathbf{E}}\approx 750mV$ , $T=300K$ when , $\frac{\partial {\mathbf{V}}_{BE}}{\partial \mathbf{T}}\approx -1.5\mathbf{m}\mathbf{V}/\mathbf{L}$, Transistor voltage V_BE have Negative temperature coefficient .

Positive temperature coefficient voltage （PTAT）

   When two bipolar transistors （BJT） Operating at unequal current densities , So the base - Of emitter voltage Difference value $\Delta$V_BE It is directly proportional to the absolute temperature （PTAT）.

   As shown in the figure above , If two identical transistors are biased with collector currents of $n{I}_0$ and $I_0$, And ignore their base currents , that $\Delta$V_BE It can be expressed as follows ：

   such ,$\Delta$V_BE It shows Positive temperature coefficient , And this temperature coefficient has nothing to do with the characteristics of temperature and collector current .
 

Summary

   Here we are , We know about bipolar transistors (BJT) Temperature characteristics of ：
   （1）CTAT :V_BE Inversely proportional to the absolute temperature , Show Negative temperature coefficient .
   （2）PTAT : $\Delta$V_BE Directly proportional to the absolute temperature , Show Positive temperature coefficient .
   （3） Pass through 、 Weighted superposition of negative temperature coefficient , You can get Zero temperature coefficient .

Two 、 Typical bandgap reference structure

   Bandgap reference , By aligning 、 Current or voltage with negative temperature coefficient superposition , Can produce almost unaffected by the process 、 Supply voltage and temperature （PVT） Constant current or voltage affected . among , It is a reference source composed of superposition of different temperature coefficients in the form of current , be called Current mode . The reference source is formed by superimposing different temperature coefficients in the form of voltage , be called Voltage mode .

（1） Voltage mode structure
   Voltage mode bandgap reference circuit , Its output is a voltage with a negative temperature coefficient VBE And PTAT The voltage drop of the current on the resistance is superimposed to produce . The following figure shows a common voltage mode bandgap reference structure .

   chart 2.1 It is the voltage reference of operational amplifier mode , Because of the op amp “ Deficiency ” The characteristics are $V_X=V_Y$ . When $R_1=R_2$ when , The collector current flowing through the two transistors is the same , Then there are

  because $\Delta V_{BE}=V_T\mathbf{l}\mathbf{n}n$, So get $V_{OUT}$ The expression of

   It can be seen from the above formula ,$V_{BE(Q1)}$ With negative temperature coefficient ,$(R1/R3)V_T\mathbf{l}\mathbf{n}n$ Is the positive temperature coefficient , As long as the reasonable setting R₁、R₂ and n The output voltage that does not change with temperature can be obtained $V_{OUT}$

   For the voltage reference circuit of current mirror structure , The structure uses current mirror to generate equipotential . In the figure M1,M2 It is an equal proportion current mirror , The same size , and M4 Tube and M5 Tubes have the same current and have the same size , Therefore, their source potentials are the same, i.e $V_X=V_Y$ , So the resistance R1 The pressure drop across the is $V_{BE(Q1)}-V_{BE(Q2)}$. Thus in R₁ It's on PTAT electric current , The current is mirrored in the resistor R₂ It's generated PTAT voltage , and Q3 The base of the tube - Emitter differential pressure $V_{BE（Q3}$ Is the negative temperature coefficient voltage , So each has positive 、 The voltage with negative temperature coefficient is added , Output reference voltage $V_{OUT}$.

(2) Current mode
   Current mode structure , As the name suggests, it is a bandgap reference circuit based on current superposition , The current with opposite temperature coefficient is superimposed according to different weights , Finally, the reference current with zero temperature coefficient is obtained . The following figure shows the current mode reference circuit with operational amplifier .

   chart 2.3 in ,Q1,Q2 Bipolar transistor , Its emitter area ratio is 1/n, And $R_2=R_3$, Due to the of op amp “ Deficiency ” Features make $V_X=V_Y$ , Again because M1,M2,M3 Same size and same gate source voltage , So it has the same current , namely $I_{D1(M1)}=I_{D2(M2)}=I_{D3(M3)}$. stay R₁ A current with a positive temperature coefficient is generated on the branch $I_{PTAT}=V_T\mathbf{l}\mathbf{n}n/R_1$, In resistance R2,R3 The branch generates a current with a negative temperature coefficient $I_{R2}=I_{R3}=V_{BE(Q1)}/R_2$, Last $I_{R1}$ And $I_{R2}$ The zero temperature coefficient current is obtained by superposition $I_{D2(M2)}$, Then it is copied to through the overcurrent mirror M3 Access Rd , By selecting the appropriate R1 and R2, The reference current with zero temperature coefficient can be obtained .

   Adjust the load resistance R4 Value , The reference voltage of any size can be obtained , This is also the advantage of current reference .