frequency responsefaculty.weber.edu/snaik/ece3120/02ch9partc_highfreqresp.pdf22 ece 3120...

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ECE 3120 Microelectronics II Dr. Suketu Naik

Chapter 9

Frequency Response

PART C:

High Frequency

Response

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Discrete Common Source (CS) Amplifier

Goal: find high cut-off frequency, fH

fH is dependent on

internal capacitances

Vo

Load Resistance

will affect fH

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9.5.1 High Frequency Model of CS Amplifier


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Miller Effect or Miller Multiplier K

Impedance Z can be replaced with two impedances:

Z1 connected between node 1 and ground = Z/(1-K)

Z2 connected between node 2 and ground = Z/(1-1/K)

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High-frequency model

C1 = Cgd(1-K), C2 = Cgd(1-1/K)

K =small signal gain= V0/Vgs=1+gmRL’; RL’=ro||RD||RL

Vo

Vo

Miller

Effect


𝑹𝒔𝒊𝒈′=Rsig||RG

𝑹𝑳′ = 𝒓𝒐| 𝑹𝑫 |𝑹𝑳

input

resistance output

resistance

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Estimating fH

𝑹𝒔𝒊𝒈′ = 𝑹𝒔𝒊𝒈||𝑹𝑮

𝑪𝒊𝒏 = 𝑪𝒈𝒔+ 𝑪𝟏𝑪𝟏 = 𝑪𝒈𝒅 𝟏 + 𝒈𝒎𝑹𝑳

′


𝑨𝑴 = −𝑹𝑮

𝑹𝑮 + 𝑹𝒔𝒊𝒈𝒈𝒎𝑹𝑳

′

AM

fH: First Estimate (Miller’s Approximation)

Miller Effect

𝒇𝑯 =𝟏

𝟐𝝅𝑪𝒊𝒏𝑹𝒔𝒊𝒈′

Mid-band Gain

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Ex9.8

Compare AM and fH with the ones found in example 9.3

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9.5.2 Analysis Using Miller’s Theorem

High-frequency model with Load Capacitance CL

What is Load

Capacitance?

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Estimating fH

AM

fH: Second Estimate (Miller’s Theorem)

𝒇𝑯 =𝟏

𝟏𝒇𝒑𝒊𝒏

𝟐+𝟏

𝒇𝒑𝒐𝒖𝒕𝟐

𝟏/𝟐

𝒇𝒑𝒊𝒏 =𝟏

𝟐𝝅𝑪𝒊𝒏𝑹𝒔𝒊𝒈′𝒇𝒑𝒐𝒖𝒕 =

𝟏

𝟐𝝅𝑪𝑳′𝑹𝑳′

𝑹𝒔𝒊𝒈′ = 𝑹𝒔𝒊𝒈||𝑹𝑮

𝑪𝒊𝒏 = 𝑪𝒈𝒔+ 𝑪𝒈𝒅 𝟏 + 𝒈𝒎𝑹𝑳′


𝑪𝑳′ = 𝑪𝑳+ 𝑪𝒈𝒅 𝟏 + 𝟏/(𝒈𝒎𝑹𝑳′ )

C1 C2

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Example 9.5

Transfer function

First approximation

Second

approximation

Exact Value

-3 dB frequency

= 9537 rad/s

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Estimating fH

AM

fH: Third Estimate (Open Circuit Time Constants)

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P9.60, P9.61: CS Amp

Omit the % contribution. Just calculate fH

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Discrete Common Emitter (CE) Amplifier

Vo


fH is dependent on

internal capacitances

Load Resistance

will affect fH

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High Frequency Model of CE Amplifier


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High-frequency model

Vo


𝑹𝒔𝒊𝒈′=Rsig||RG

𝑹𝑳′ = 𝒓𝒐| 𝑹𝑪 |𝑹𝑳

input

resistance output

resistance

C1 C2

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Estimating fH

𝑨𝑴

= −𝑹𝑩

𝑹𝑩+ 𝑹𝒔𝒊𝒈

𝒓𝝅𝑹𝑩||𝑹𝒔𝒊𝒈 + 𝒓𝒙 + 𝒓𝝅

𝒈𝒎𝑹𝑳′

AM

fH: First Estimate (Miller’s Approximation)

Miller Effect

𝒇𝑯 =𝟏

𝟐𝝅𝑪𝒊𝒏𝑹𝒔𝒊𝒈′

Mid-band Gain

𝑹𝒔𝒊𝒈′ =

𝒓𝝅 ||[𝒓𝒙+ (𝑹𝑩| 𝑹𝒔𝒊𝒈 ]

𝑪𝒊𝒏 = 𝑪𝝅+ 𝑪𝟏

𝑪𝟏 = 𝑪𝝁 𝟏 + 𝒈𝒎𝑹𝑳′

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Ex9.10

Note the trade-off between gain and bandwidth

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9.5.2 Analysis Using Miller’s Theorem

High-frequency model with Load Capacitance CL

What is Load

Capacitance?

Vo

C1

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Estimating fH

AM

fH: Second Estimate (Miller’s Theorem)

𝒇𝑯 =𝟏

𝟏𝒇𝒑𝒊𝒏

𝟐+𝟏

𝒇𝒑𝒐𝒖𝒕𝟐

𝟏/𝟐

𝒇𝒑𝒊𝒏 =𝟏

𝟐𝝅𝑪𝒊𝒏𝑹𝒔𝒊𝒈′ 𝒇𝒑𝒐𝒖𝒕 =𝟏

𝟐𝝅𝑪𝑳′𝑹𝑳′

𝑹𝑳′ = 𝒓𝒐| 𝑹𝑪 |𝑹𝑳

𝑪𝑳′ = 𝑪𝑳 + 𝑪𝝁 𝟏 + 𝟏/(𝒈𝒎𝑹𝑳′ )

C1

C2

𝑹𝒔𝒊𝒈′ =

𝒓𝝅 ||[𝒓𝒙+ (𝑹𝑩| 𝑹𝒔𝒊𝒈 ]

𝑪𝒊𝒏 = 𝑪𝝅+ 𝑪𝝁 𝟏 + 𝒈𝒎𝑹𝑳′

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Estimating fH

AM

fH: Third Estimate (Open Circuit Time Constants)

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P9.64, 9.65: CE Amp

Omit the % contribution. Just calculate fH

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Summary

Low Frequency Response:

The coupling and bypass capacitors cause the amplifier gain

to fall off at low frequencies

The low cut-off frequency can be estimated by considering

each of these capacitors separately

High Frequency Model:

Both MOSFET and the BJT have internal capacitive effects

that can be modeled by augmenting the device hybrid-π

model with capacitances.

Transition Frequency indicates the speed of the transistor

MOSFET: fT = gm/2π(Cgs+Cgd)

BJT: fT = gm/2π(Cπ+Cμ)

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A figure-of-merit for the amplifier is the gain-bandwidth product

(GB = AMfH): tradeoff between gain and bandwidth while

keeping GB

High Frequency Response:

The internal capacitances of the MOSFET and the BJT cause the

amplifier gain to fall off at high frequencies.

An estimate of the amplifier bandwidth is provided by the

frequency fH at which the gain drops 3dB below its value at mid-

band (AM).

The high-frequency response of the CS and CE amplifiers is

severely limited by the Miller effect

Three methods: 1) Miller’s Approximation, 2) Miller’s Theorem,

3) Open-circuit Time Constants

Summary

frequency responsefaculty.weber.edu/snaik/ece3120/02ch9partc_highfreqresp.pdf22 ece 3120...

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