# Bandgap reference circuit

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Bandgap reference circuit
307暑期訓練課程 各位同學們好，這次要上課的主題為Bandgap reference circuit Bandgap reference circuit

General Considerations
To generate a voltage or current reference that is independent of the supply voltage and process and has a well-defined behavior with temperature. The required temperature dependence assumes one of three forms : Proportional to absolute temperature (PTAT) Constant-Gm behavior Temperature independent 一般來說在類比電路中常常會需要使用到多個參考電流或是電壓源 比較常見的有下列三種： PTAT, constant-gm, 以及與溫度無關的參考電流電壓源

General Considerations
The sensitivity of a parameter y to a second one x is defined as The variation of a parameter y that results from changes in temperature is usually characterized by its fractional temperature coefficient, which is defined as the fractional change per degree centigrade change in temperature 首先讓我們先定義sensitivity 一般來講會用到的是Temperature coefficient，主要是量測溫度改變下，電壓的變化量百分比

Simple Current Sources
The output current of the circuit is quite sensitive to VDD 我們以一個簡單的電流源做為例子 經由公式的推導可以發現IC2的TC是VCC的TC-R的TC 所以這個簡單電流源的溫度係數是容易受到VCC跟R的影響

Supply-Independent Biasing
Supply-Independent Current Generator (ΔVGS reference) Output current is determined by K and RS The current is independent of the supply voltage, but still a function of process and temperature. 再來我們介紹一種跟supply無關的偏壓方法 這種偏壓方法產生的電流源跟Rs以及K有關 而RS和K通常會容易受到溫度以及製程影響，所以此種篇壓方法容易受製程飄移的影響

Temperature independent References
If a reference is temperature independent, then it is usually process-independent as well. If two quantities having opposite temperature coefficients (TCs) are added with proper weighting, the result displays a zero TC. To obtain a reference voltage with zero TC 接下來介紹另一種與溫度無關偏壓方法 主要想法是將一個與溫度負相關的CTAT電壓源跟一個與溫度正相關的PATA電壓源 兩者做相加，最後產生與溫度沒有相關的電壓源

Temperature independent References
The forward voltage of a PN-junction diode exhibits a negative TC. 這邊是推導VBE對溫度做微分後的結果 可以發現VBE是負的溫度係數 也就是CTAT

Temperature independent References
PTAT Generator If two identical transistors (IS1 = IS2) are biased at collector currents of nI0 and I0 , and their base currents are negligible Thus, VBE difference exhibits a positive temperature coefficient 這邊是推導VBE的差值對溫度微分的結果 可以發現delta VBE是具有正的溫度係數

Bandgap reference example
Kujik Bandgap reference Vos is amplified by 1+R2/R3 Vos itself varies with temperature, raising the temperature coefficient of the output voltage. 經由以上的推導結果 利用VBE與delta VBE做相加 跨在R2的跨壓VR2是跟delta VBE有關的 這樣可以做出一個與溫度無關的參考電壓源

Bandgap reference example

Bandgap reference Output Issues

Bandgap reference schematic

Bandgap reference schematic

Bandgap reference schematic

Bandgap reference Specs.
Parameter Specification Technology CIC 0.18um Supply voltage 1.8v Reference voltage Static current Consumption 26.3uA VDD=1.8v 25ppm/℃ 10kHz 90.3dB 這邊是最後的performance表 麻煩兩天後present時，附上上一頁的圖與這個表 謝謝