2/DC condR l a DC signal, 傳導電流流過整個導體橫截面.

AC signal, 交變的載流子形成交變磁場, 該磁場又感應一個電場,

與該電場相關聯的電流密度與原始的電流相反,在中心感應最強,

所以導體中心的電阻最大, 隨著頻率的提高, 電流趨向於導體外部—skin depth.

Passive Component RF Behavior

2

0 1/ 2 , where .z condJ pIJ pr aJ pa p j

So z-dir current density Jz can be represented by

Fig.

Schematic cross-sectional

AC current density representation

normalized to DC current density.

p.s.

Normalized resistance and

Inductance under high-freq.

Conditions (f > 500 MHz)

,2

,2

where 1/ .

DC

DC

cond

R a

R

L a

R

f

1

1/ex

a

Z j Lj C R

Ca 為寄生電容(模擬電荷分離)

Cb為寄生電容(模擬內部引線電容),

L = Lex等效引線電感知道 Ca, L 就可計算出等效阻抗

Fig. Electric equivalent circuit

representation of the resistor.

Chip R (at high frequency)

b aC C

parasitic capacitance Ca = 5 pF

0 2ln 1

2ex

l lL

a

1. at low freq. the impedance of the resistor is

equal to R.

2. As the freq. > 100 MHz, the effect of the stray

capacitance becomes dominant, which causes

the impedance of the resistor to decrease.

3. Beyond the resonance at 20 GHz, the total

impedance increases due to the lead inductance.

p.s. picture depend on each R case

Chip C (at high frequency)

Fig. Electric equivalent circuit

for a high-frequency capacitor.

Higher freq, dielectric become lossy

(there is a conductor current flow).

1ex s

e

Z j L RG j C

L 為寄生引線電感Rs為寄生引線串聯Ohmic loss

Re 等效介質損耗電阻(高頻介質有 )loss tangen tant die

tan 1/diee e

AG C R

d

0

2 2s DC

Cu

fa lR R

a

p.s. picture depend on each C case

Chip L (at high frequency)

Fig. Equivalent circuit of the

high-frequency inductor.

( )s sZ j L R C

s d

s d

R R

C C

1. The inductor acts as like an ideal inductance at

low freq.

2. The impedance of the inductor increases more

rapidly as the freq. approaches resonance (self-

resonant frequency : SRF).

3. After the freq. passes the SRF , the influence of

the parasitic capacitance Cs becomes dominant.

=> the impedance of the coil decreases.

p.s. picture depend on each L case

Cs 為寄生並聯電容

Inductors for RF circuits

Table. Examples of inductor applications in each circuit block of a mobile phone

高頻電感三大功能

Murata(RF元件大廠)在製造電感時把Chip L依用途分為三類

1. high-frequency(RF) circuits,

2. power supply line inductors (power inductors),

3. inductors for general circuits.

現在我們來談一下手機最常見的inductor for RF circuits.

Used in the high-frequency band from 10 MHz to several GHz.

As these products require a high Q value, most have a non-magnetic core structure.

Mainly used in the high-frequency circuits of mobile communications equipment,

such as mobile phones, wireless LAN, and others.

Properties

Winding copper wire in a spiral shape around an alumina core.

Thicker wire than the multilayer and film structures, which provides the following features:

1) Low DC resistance is possible.

2) Extremely high Q value.

3) Large currents can be supported.

These features make the wire wound structure suitable for matching applications in antenna

and PA circuits that require an extremely high Q factor, and resonance applications in IF circuits.

Inductors for RF circuits 3 different structure (I) wire wound structure

Inductors for RF circuits 3 different structure (II) multilayer structure

Layering ceramic materials and coil conductor to create an integrated monolithic-type inductor.

Smaller size and lower cost compared to the wire wound structure.

Q factor is lower than wire, but provides good overall balance between the

L value deviation, rated current, size, price, and other characteristics.

Suitable for various applications such as RF circuit matching, choke, and resonance for mobile

communication equipment.

Inductors for RF circuits 3 different structure (III) film structure

Also a multilayer structure, but the coil is formed with high accuracy over ceramic materials.

Extremly accurate cores providing the following features:

1) High-performance electrical characteristics can be realized even for compact chips (0402 size).

2) Stable inductance and small inductance value steps are supported.

3) High Q and high SRF.

Narrow deviation and a high Q factor to support trends toward smaller and more lightweight mobile.

Wire wound inductors feature a high Q value.

High Q values are used in the matching circuits because their high Q values give them excellent

attenuation characteristics inside the pass band of the filters.

Matching applications of antennas for maintaining the Tx and Rx sensitivity of the antennas.

Low Rdc characteristics (high current levels flow), also employed in choke circuits.

Micromachining of the coil is enabled by forming the electrodes using a photolithography technique.

Smaller sizes and high Q characteristics mainstream 0603 and 0402 size.

Used in the matching and resonance circuits of RF units that require miniaturized sizes, minimal

deviation in inductance and finely graded inductance levels.

Also used in choke circuits that demand miniaturized sizes and low Rdc.

Multilayer inductors have the lowest Q value of the three structures.

They feature a good overall balance in terms of the inductance value line-up, size and cost, and are

used in the matching and resonance circuits of RF units and in all kinds of choke circuits.

Inductors for RF circuits Applications (I)

Inductors for RF circuits Applications (II)

Cross-sectional view of a typical chip resistor

Actual construction of a surface-mounted ceramic multilayer capacitor

1. WCDMA在Uplink採BPSK, Downlink採QPSKPulse shaping採RRC(Root-Raised-Cosine)就是為了防止無線傳輸信號所產生的ISI (Inter Symbol Interference)那引起ISI最主要原因就是Group Delay簡單講就是訊號沒有同步造成Group Delay過大引起ISI

2.為了消除ISI, 引入Pulse shaping技術主要目的就是消除雜訊,方便解調而WCDMA所採用的就是RRC Filter

RRC Filter的時域圖就是著名的Broadcom logo在數學上,就是一個 sinc function

3. LTE在Uplink採SC-FDMA, Downlink採OFDMAOFDM會更有效率的使用頻寬,並且容納更多人而他的每一個sub-carrier就是Broadcom logo並且互相正交叫Multiple OFDM.

近期大事回顧

FFT

RF Block Diagram