A high PSRR CMOS bandgap voltage reference

ZHOU Qian-neng，DUAN Xiao-zhong，LIHong-juan

(1.School of Electronic Engineering，Chongqing University of Posts and Telecommunications，Chongqing 400065，China;2.National Labs of Analog Integrated Circuit，Sichuan Institute of Solid－State Circuits，Chongqing 400060，China;

3.School of Computer Science and Technology，Chongqing University of Posts and Telecommunications，Chongqing 400065，China)

1 Introduction

Voltage reference is an important circuit block in many analog and mixed－signal system－on－chip(SoC)applications such as data converters，DC－DC converter，DRAMs and flash memory controlling blocks and so on[1－5].It should be free from fluctuations of process，power supply voltage，and temperature.In fact，the bandgap reference(BGR)is one of themost popular voltage reference，whose output is usually a weighted sum of the base－emitter voltage VBE of a diode－connected bipolar transistor and the thermal voltage VT.For the bandgap reference in modern SoC design，it is necessary to achieve high power supply rejection ratio(PSRR)over a broad frequency range in order to reject noise from the high speed digital circuits on the chip.

In the recent past，many techniques have been reported to improve PSRR of BGR[6－10].However，to further improve the performance of BGR，the high PSRR BGR must still be analyzed and discussed.

In this paper，a BGR，which adopts a pre－regulator，is presented.The designed BGR with preregulator has a simple architecture and achieves well performance.In section 2，the analysis of BGR without pre－regulator will be discussed.The analysis and design of BGR with pre－regulator will be given in section 3.Section 4 will give the simulation results.Finally，the conclusion is given in section 5.

2 Analysis of BGR without Pre－regulator

Figure1 shows the BGR without pre－regulator，which consists of transistors M1～M18，vertical pnp transistors Q1～Q2，and resistors R1～R6，and allMOS transistors work in strong inversion.The circuit of BGR is similar to that reported in reference[5]，but whose error amplifier is folded cascade amplifier instead of the two－stage amplifier in reference[5].In this paper，All MOS transistors adopt the long channel transistors so that the channel－length modulation effect is negligibly small.

Figure 1 BGR without pre－regulator

In Figure 1，transistors M4～M18and resistors R5～R6form the error amplifier，and which keeps the voltages VAand VBbe equal，i.e.VA=VB.Here，VAand VBare，respectively，the voltage of node A and node B.M1，M2and M3are entirely same，so they have the same drain current，i.e.I1=I2=I3.R2and R3are entirely same，and Q1has an emitter area that is n times that of Q2.So，the output voltage of the BGR，i.e.Vref，can be expressed as where，Veb2is the emitter－base voltage of Q2，VTis the thermal potential and can be expressed as

where，k is Boltzmann’s constant，q is electronic charge，T is absolute temperature.In Eq.(1)，Veb2has a temperature coefficient of－2.2mV/°C at 25°C，while VThas a temperature coefficient of+0.085mV/°C.can be achieved by proper choice of R2/R1and n at25°C.However，the BGR cannot be applied effectively to SoC designs be-cause that it cannot achieve high PSRR over a broad frequency range.So，a BGR，which adopts pre－regulator to improve its PSRR，will be designed in the next section.

3 Analysis and Design of BGR with Pre－regulator

As shown in Figure 2，the designed BGR with pre－regulator consists of a pre－regulator，the core circuit of BGR and a start－up circuit.The core circuit of BGR with pre－regulator is similar to that circuit in Figure 1，but whose operating supply voltage is the internal regulated supply voltage Vreginstead of the power supply voltage Vdd.The core circuit of BGR with pre－regulator generates a bandgap reference voltage Vref，and has a good temperature characteristic，whose analysis is similar to that in Section 2.To simplify the analysis，this section will not discuss the core circuit of BGR with pre－regulator in detail.There are two possible equilibrium points in the circuit of BGR，so a startup circuit is necessary.As shown in Figure 2(A)，the startup circuit ismade up of transistor Ms1～Ms5.The pre－regulator will provide an internal supply voltage Vreg，which makes the operating supply voltage of core circuit of BGR be the output voltage Vregof pre-regulator instead of power supply voltage Vdd.Therefore，the PSRR of Vrefwill be improved and will be quantitatively analyzed as following.

Figure 2 BGR with pre－regulatior(A)start－up circuit;(B)Pre－regulator;(C)Core circuit of BGR

As shown in Figure 2(B)，the pre－regulator，which ismade up of M19～M26，is adopted to achieve a high PSRR over a wide frequency range.And all MOS transistors are in strong inversion.For convenience，it is assumed that iiand gmiare，respectively，the small－signal current and transconductance of transistor Mi.M1～3，and M19are the entirely same，so it is concluded thahave the same aspect ratio respectively，so it concluded thatare entirely same，and Q1has an emitter area that is n times that of Q2.Assumed that there is an incremental voltage variation vregat node VREG，so there are incremental voltage variation va，vband vcat node A，node B and node C respectively.vaand vbcan be expressed as

where，re1and re2are，respectively，the emitter resistor of Q1and Q2，r1and r2are，respectively，the resistance value of resistor R1and R2.Eq.(3)and Eq.(4)indicate that va＜vb.The error amplifier，which ismade up of M4～M18and R5～R6，has a small signal gain Ad，so the voltage variation vcat node C has that vc=Ad×(vb－va).According to Eq.(3)and Eq.(4)，vdcan be expression as

where，

So，

In the similar way，the following expression can be obtained as

According to the Kirchhoff current law(KCL)at node vreg，the following equation can be obtained as

where，Vddis the incremental voltage variation of power supply voltage Vdd，γ0.25is the source－drain resistance of the transistor M25.According to Eq.(3)～Eq.(12)，the following expression can be obtained

In the similar way，the output voltage variation Vrefof BGR with pre－regulator can also be written as

So，the PSRR of BGR with pre－regulator can be expressed as

This equation indicates that the designed BGR with pre－regulator achieves an improved PSRR.

4 Simulation Results

To verify the functionality of the BGR with－and without－pre－regulator，they are designed and simulated in CSMC 0.5μm CMOSprocesswith 3V power supply voltage.

Figure 3 Simulated output voltage of BGR with－and without－pre－regulator versus temperature

Figure 3 shows the output voltage Vrefof BGR with－and without－pre－regulator as a function of temperature with 3V power supply.Simulation results show that BGR without－and with－pre－regulator have，respectively，an output voltage variation about 581.6μV and 576μV when temperature ranging from－15℃to 90℃.Figure 4 shows the simulated PSRR of BGR with－and without－pre－regulator.BGR without pre－regulator achieves－81.82 dB，－81.8 dB，80.1 dB，－64.8 dB and－44.9 dB at10 Hz，100 Hz，1 kHz，10 kHz and 100 kHz respectively，and BGR with pre－regulator achieves－117.8 dB，－117.3 dB，－106.2 dB，－86.5dB and－66.2dB at 10 Hz，100 Hz，1 kHz，10 kHz and 100 kHz respectively.Figure 5 shows the output voltage Vrefas a function of the power supply voltage Vdd.When power supply voltage Vddranging from 2.2 V to 8 V，the output voltage of BGR without－and with－pre－regulator have，respectively，a variation of 4.28 mV and 9.73μV.Finally，the performances of BGR withand without－pre－regulator are summarized in Table 1.Simulation results show that the designed BGR with pre－regulator achieves a well PSRR by adopting pre－regulator circuits.

Figure 4 Simulated PSRR of BGR with－and without－pre－regulator versus frequency

Figure 5 Simulated output voltage of BGR with－and without－pre－regulator versus power supply voltage

Table 1 Performances of BGR with－and without－pre－regulator

5 Conclusion

CMOS bandgap references with－and withoutpre－regulator is designed and analysised in this paper.The high PSRR BGR is achieved by adopting a pre－regulator.Simulation results show that the BGR with pre－regulator achieves excellent stability，relatively small temperature dependency and relatively well PSRR.The designed BGR with pre－regulator is well suited for analog and mixed－signal SoC applications.

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