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Lecture 25 Multistage (II) DC AND CURRENT SOURCES

Outline

1. DC Voltage Sources 2. DC Current Sources and Sinks

Reading Assignment: Howe and Sodini, Chapter 9, Sections 9-3-9.4

6.012 Spring 2007 Lecture 25 1 1. DC Voltage Sources Characteristics of DC Voltage Sources :

• A well controlled output voltage • Output voltage does not depend on current drawn from source ⇒ Low Thevenin Resistance

Consider a MOSFET connected in “ configuration”

I-V characteristics: W W I = µ C ()V − V 2 = µ C ()V − V 2 D 2L n ox GS Tn 2L n ox DS Tn Beyond the threshold voltage, the MOSFET looks like a “diode” with quadratic I-V characteristics

6.012 Spring 2007 Lecture 25 2 How does one synthesize a with this? Assume a is available

VGS = VDS takes a value needed to sink current W 2 i = I + i = µ C ()v − V D REF OUT 2L n ox OUT Tn Then: W 2 i = µ C ()v − V − I OUT 2L n ox OUT Tn REF

Solving for vOUT: IREF + iOUT vOUT = VTn + W µnCox 2L

6.012 Spring 2007 Lecture 25 3 Synthesizing Voltage Sources (contd.)

vOUT is a function of IREF and W/L of MOSFET:

•IREF ↑⇒vOUT ↑ •W/L ↑⇒ vOUT ↓

Small Equivalent Circuit Model:

1 1 Rout = || ro ≈ gm gm

Rout is small (good!)

6.012 Spring 2007 Lecture 25 4 PMOS voltage source

Same operation and characteristics as NMOS voltage

source. PMOS needs to be larger to attain the same Rout.

6.012 Spring 2007 Lecture 25 5 3. DC Current Sources and Sinks Characteristics of Current Sources • A well controlled output current • Supplied current does not depend on output voltage ⇒ High Norton Resistance Connect a voltage source to the gate of another MOSFET: 1⎛ W⎞ 2 IOUT ≈ ⎜ ⎟ µnCox()VREF −VTn 2⎝ L⎠ 2 1 ⎛ W⎞ 2 IREF ≈ ⎜ ⎟ µnCox ()VREF − VTn 2 ⎝ L ⎠ 1

⎛ W⎞ ⎜ ⎟ ⎝ L ⎠ Then: I = I 2 OUT REF ⎛ W⎞ ⎜ ⎟ ⎝ L ⎠ 1

IOUT scales with IREF by W/L ratios of two ⇒ Circuit

Well “matched” important.

6.012 Spring 2007 Lecture 25 6 DC Current Sources and Sinks (contd.)

Small Signal Equivalent Circuit Model:

Rout 2 = ro2

I-V characteristics of NMOS current source:

6.012 Spring 2007 Lecture 25 7 PMOS Current Source

• NMOS current source sinks current to ground • PMOS current source sources current from positive supply

PMOS Current Mirror:

6.012 Spring 2007 Lecture 25 8 3. Multiple Current Sources Since there is no DC gate current in MOSFET, we can tie up multiple current mirrors to single current source:

⎛ W⎞ ⎜ ⎟ ⎝ L ⎠ I = I n OUTn REF ⎛ W⎞ ⎜ ⎟ ⎝ L ⎠ Similar idea with NMOS current sinks: R

6.012 Spring 2007 Lecture 25 9 Multiple Current Sources and Sinks

Often, in a given circuit, we need current sources and sinks. We can build them all out of a single current source.

⎛ W ⎞ ⎛ W⎞ ⎜ ⎟ ⎜ ⎟ ⎝ L ⎠ ⎝ L ⎠ I = I 1 I = I 2 OUT1 REF ⎛ W⎞ OUT2 REF ⎛ W⎞ ⎜ ⎟ ⎜ ⎟ ⎝ L ⎠ R ⎝ L ⎠ R ⎛ W⎞ ⎛ W⎞ ⎛ W⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ L ⎠ ⎝ L ⎠ ⎝ L ⎠ I = I 4 = I 4 1 OUT4 OUT1 ⎛ W⎞ REF ⎛ W⎞ ⎛ W⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ L ⎠ 3 ⎝ L ⎠ 3 ⎝ L ⎠ R

6.012 Spring 2007 Lecture 25 10 Generating IREF Simple circuit:

V − V I = DD OUT REF R

IREF VOUT = VTn + W µnCox 2L

VDD − VTn For large W/L: I ≈ REF R • Advantages

–IREF set by value of • Disadvantages

–VDD also affects IREF.

–VTn and R are functions of temperature ⇒ IREF(T). In the real world, more sophisticated circuits are used to

generate IREF that are VDD and T independent.

6.012 Spring 2007 Lecture 25 11 What did we learn today?

Summary of Key Concepts

• Voltage source easily synthesized from reference current source using MOSFET in diode configuration • Current source easily synthesized from current source using current mirror circuit. • Multiple current sources and sinks with different magnitudes can be synthesized from a single current source. • Voltage and current sources rely on the availability of well “matched” transistors in IC technology.

6.012 Spring 2007 Lecture 25 12