Diode CircuitsBy

Professor Syed Idris Syed Hassan

Sch of Elect. & Electron Eng

Engineering Campus USM

Nibong Tebal 14300

SPS Penang

Application of diodes

• Rectifier

• Detector

• Mixer

• switching/switch

• Phase shifter

• Attenuator

Type of diodes

p-n junction Diode Detector, mixer,modulator(slow response)

Schottky barrier diode Detector, mixer,modulator (fast response)

PIN diode Switching, attenuatorcurrent controller

VARACTOR Tuner, harmonicgenerator, frequencymultiplier, VCO,parametric amplifier.

Basic diode characteristic

IV+

-

I

V

Is

+

-

Id

V d C p

Lp

C j(V) R j(V)

V-I characteristic Equivalent circuit

1)( Vs eIVI where= q /nkT , q =charge, k=Boltzmann’s

constant, T = temperature, n = ideality factor and Is = saturation current.

Package components

Rs Junction components

Contact resistance

ContinueLet’s say diode voltage V = Vo + where Vo is a DC bias voltage and is a small AC signal voltage. We expand using Taylor series

n

nnR

n

axaf

axafaxafafxf

)!1(

))((....

))((!2

1))(()()(

1)1(

2"'Taylor series

By substituting, we have (x-a) = ( Vo+ -Vo)= and the Taylor series for I(V) is

Taking f(x) = I(V), then x= Vo+ and a = Vo

1)( Vs eIVI 1)( oV

soo eIVII

....2

1)(

2

22

oo VVo

dV

Id

dV

dIIVI

where and

Reminder

ContinueBy substituting and Io= I(Vo) in the first derivative

j

dsoV

sV R

GIIeIdV

dI o

o

1

Similarly in the second derivative, we have

'222

2

ddsoV

sV

d

V

GGIIeIdV

dG

dV

Id o

oo

1)( Vs eIVI

...2

)( '2

ddo GGIVIThen (400)

1)( oVsoo eIVII

where

Rectifier application

If the diode voltage consist of DC and small RF signal V = Vo + costwhere Vo is a DC bias voltage and cos ot is a small RF signal voltage. Then by substituting into (400)

....cos2

cos)( 2'2

tGtGIVI odo

odoo

RF in DC out

....2cos44

cos '2

'2

tGGtGI odo

do

odoo

continue

Rearrange

....2cos4

cos4

)( '2

'2

tGtGGIVI odo

ododo

o

DC rectified current

AC harmonics current of frequency o

and 2o. This can be filtered off by using lowpass filter

Detector application

ttmV omo coscos1

Modulated RF Detected RF

Modulated signal representation

where m = modulation index

m= modulation frequency

o= RF carrier frequency

continue

....coscos12

coscos1)(

22'2

ttmG

ttmGIVI

omdo

omdoo

tt

tm

mtm

ttm

tmm

G

tm

tm

tGI

mom

mom

omomo

ommdo

momoodoo

2cos2cos

2cos2

2cos2cos

2cos2cos2

cos22

14

cos2

cos2

cos

44

2

22'

2

22

Trigonometry relationship yxyxyx coscos

2

1sinsin

yxyxyx coscos2

1coscos

yxyxyx sinsin2

1cossin

yxyxyx sinsin2

1sincos

xx 2cos1sin2 2

xx 2cos1cos2 2

continueFrom the eq. above we have several harmonics as shown with relative amplitude.

Am

plitu

de

0 m

2m

o-

m

o

o

m

o m

)

o

o

m)

o

m

)

o

m)

1+m 2/2

2m

m 2/2

mm

1+m 2/2

m 2/4m 2/4

k

km/2km/2

k=oGd/(o2Gd’/4)

=4/(o)

As linear detector( ~oGd)

As squared detector ~o2Gd’/4

Square-law region of diode detectorWe are measuring power , thus square-law region is to be chosen since the power measured is proportional to o

2. If we want to measure voltage , then the linear region is the choice. For linear detector,we choose frequency at o

and for square-detector at 2o.. Using filter we can filter out the modulating frequency m.

logP in

(dBm)

log v out

Saturation

Noise level

Square-law region

1V

V out = o2=P in

100mV

10mV

1mV

100 V

10 V

-30 -20 -10 0 10 20 30

Single-ended mixerRF AMP MIxer

LocalOscillator

IF AMPLowpass

filterfRF

fRF

fLO

f IF=f RF -f LO

RF input

MIxer

LocalOscillator

Bandpassfilter

fRFf IF

fLO

f IF=f RF +f LO

IF input

RF AMP

Downconverter

Upconverter

The purpose of mixer is to convert either from one frequency to higher frequency or vice versa. The advantages of conversion are (i) to reduce 1/f noise when convert to lower frequency (ii) for easy tuning for a wide band with fixed IF and (iii) frequency off-set between transmitter and receiver by using a single LO as in Radar.

Simplest Single-ended mixer

•Uses nonlinearity of a diode property•The output generated consist of frequencies spectrum dc component, r,o,r-o, r+o.•For IF, we filter out all frequencies except r-o. •For upconverter, we filter out all lower frequencies and allow only r+o. •Combiner either T-junction or directional coupler•Matching network is to match the output of combiner to the diode circuitry.

bandpassfilter

v icos( r-o)tMatchingnetwork

Combiner

DC bias

LO

vocos ot

v rcos rt r , o ,r+ o

RFC

RFC

analysisLet’s

2coscos2

'tvtv

Gi oorr

d

Then substituting into equation (400) and we have for the second term as

tvttvvtvG

ooorrorrrd 2222 coscoscos2cos

2

'

tvv

tvvtvtvvvG

oror

ororoorrord

cos2

cos22cos2cos4

' 2222

tvv rrRF cos tvv ooLO cosand

DC

Figure of merit in mixer is its conversion loss, defined as

dBpoweroutputIF

powerinputRFavailableLc log10

Single Balanced Mixer Circuit

Advantages•For either better input SWR or better RF/LO isolation•Cancellation of AM noise from LO

* Note that, although it is not shown, the diodes required biasing and matching network.

/4

/4

Z o

Z o

Zo

Z o2/Z o

2/Z o

Z o Z o

diode

Diode

RF

LO

LPF

LFP

analysisLet’s

tvvtv

tvvtvtv

onorr

oono

orr

cossin

180cos90cos)(1

The voltages across the two diodes of 90o out of phase is given as

tvv rrRF cos ttvvv onoLO cos)(and

Where vr<<vo and vn(t)<<vo

tvvtv

tvvtvtv

onorr

oono

orr

sincos

90cos180cos)(2

Diode 1

Diode 2

Vn is a small random noise voltage

Diode currentAssuming identical diodes so that diode currents can be represented as

211 kvi

ttvvvtvvtvki ornoronorr cossin2cossin 22221

222 kvi and (reverse polarity)

ttvvvtvvtvki ornoronorr sincos2sincos 22222

ttvvv

tvvtvk

orornor

onorr

sinsin2

2cos12cos12

22

ttvvv

tvvtvk

orornor

onorr

sinsin2

2cos12cos12

22

Dc and lower frequency bands

IF frequency band

tvvvvvvk

i ornornor sin22

221

tvvvvvvk

i ornornor sin22

222

After low pass filtering, the remaining terms are dc and IF frequency terms, thus

Written the IF frequency i = r- o then the IF current is

tvkvtvvkviii iorinorIF sin2sin221

where vn << vo . This show that the noise in the first order is cancelled by the mixer while the desired IF signal combined in phase.

Anti parallel diode mixers

RF input

Bandpassfilter for RF

Lowpassfilter for LO

and IF

LO input

Lowpassfilter for IF

IFoutput

r o i

iro 2

1The LO is one-half of usual LO, I.e

The non-linearity of diode generates 2nd harmonic of LO to mix with RF(r)

to produce desired IF. The anti parallel diode creates symmetrical V-I

characteristic that suppresses the fundamental product of RF and LO. It also

suppresses AM noise.

Double Balanced mixer

180 o

hybrid

RF input

LO input

IFoutput

Z o

Single -ended mixer produces output consisted of all harmonics. The balanced mixer using hybrid suppresses all even harmonics of the LO. Double balanced mixer suppresses all even harmonics both LO and RF.

Image rejection mixer

3dBpowerdivider

RF input

Mixer A

Mixer B

90 o hybrid

LO

LSB

USB

IF out

90 o hybrid

Z o

The RF with frequencyr= o + i will also produce the IF (i) when mixed with LO. The frequency produced will be USB(r= o + i ) and LSB(r= o - i ) . The undesired frequency either USB or LSB is called image frequency. The mixer can produce one single side band is used as modulator.

AnalysisLet RF signal consist of both upper and lower sidebands

tvtvv ioLioUr coscos

tvt

vv io

Lio

UAr cos

2cos

2

Then input to mixer A and B

oio

Loio

UBr t

vt

vv 90cos

290cos

2

After mixing with LO, o , The IF’s produced by mixer are.

tkv

tkv

v iL

iUA

i cos22

cos22

oi

Loi

UBi t

kvt

kvv 90cos

2290cos

22

Analysis

Both IF , then combined in the 90o hybrid produces LSB and USB.

t

kv

tvtvtvtvk

v

iL

iLo

iUiLiULSB

cos2

cos180coscoscos4

tkv

tvtv

tvtvk

v

iU

oiL

oiU

oiL

oiUUSB

sin2

90cos90cos

90cos90cos4

Pin Diode Equivalent Circuit

C p

Lp R s R 1

C 1

PIN diode resistance

1

10

100

1000

100000.0001 0.01 1 100

Forward bias (mA)

RF

re

sist

ance

(O

hm

)0.1

1

10

100

1000

RF

co

nd

uct

ance

(m

Oh

m)

N +

I

P +

symbol

Equivalent circuits for ON and OFF states of PIN diodes

L i

R r

L i

R f

C jZ r

Z f

ONstate

OFFstate Reverse bias will provide OFF state

Forward bias will provide ON state

Single-pole PIN diode Switches

Series

+VR SW

C 1

Diode

RFC1

RFC2

C 2

Parallel

R+V

C 1

SW

RFC

Diode

C 2

RF in

RF in

RF out

RF out

ON =No RF outOFF= RF out

ON= RF outOFF=No RF out

Note: C1 and C2 are dc block

Simplified switching circuits

Z d

Z o

Z o

Z o

+V L_

+V L_

2V o

2V o Z dZ o

o

L

V

VIL log20

do

o

ZZ

ZIL

2

2log20

In general, the insertion loss

Series switch

Shunt switch

od

d

ZZ

ZIL

2

2log20

iff

jirrd LjRZ

CLjRZZ

1

where

ExampleA single-pole switch is to be constructed using a PIN diode with the following parameters: Cj= 0.1pF, Rr= 1, Rf= 5 , Li= 0.4nH. If the operating frequency is 5 GHz and Zo= 50which circuit (series or shunt) should be used to obtain the greatest ratio of off-to-on attenuation?

Solution

6.125.0

7.30511

jLjRZ

jCLjRZZ

iff

jirrd

dBZZ

ZIL

do

o 11.02

2log20

dB

ZZ

ZIL

od

d 03.02

2log20

dBZZ

ZIL

od

d 07.72

2log20

dB

ZZ

ZIL

do

o 16.102

2log20

Series switch Shunt switch

ON

OFF

state

Ratio 10.05dB Ratio

7.04dB

Other Single pole single throw PIN Switches Configuration

50

D1

D2

D1 D3

D2 50

L- SPSTSwitch

T- SPSTSwitch

Single Pole Single Throw

Note:Biasing are not shown,just diodes configuration

SPST Switches performanceT y pe Iso la tion In sertion

S eries

2

10 21log10

o

c

Z

X

o

s

Z

R

21log20 10

S h un t

s

o

R

Z

21log20 10

2

10 21log10

c

o

X

Z

L

22

2

10

12

21log10

s

o

o

c

s

o

R

Z

Z

X

R

Z

2

2

10

2

21log10

c

so

o

s

X

RZ

Z

R

T

22

10

2

10

221log10

1log10

s

c

s

o

o

c

R

X

R

Z

Z

X

2

10

2

10

21log10

1log20

c

so

o

s

X

RZ

Z

R

PIN diode switching operation

Isolation Vs Diode resistance

25

30

35

40

45

50

55

60

0 1 2 3

Diode resistance (ohm)

Iso

lati

on

(d

B)

By putting diodes in parallel will reduce the total diode resistanceand thus improves isolation as shown in graph.

AC

V

50 Switch

50

Source Load

Diode "OFF"-Switch "ON"

Diode "ON"-Switch "OFF"

Equivalent circuit

Switch Configuration

(Shunt diode)

PIN diode switch (improving isolation)

AC

V

50 Switch

50

Source

Load

Equivalent circuit

Switch Configuration

4

AC

2550

1 50

Isolation vs line length

354045

5055606570

758085

0 100 200

Line length(deg)

Iso

lati

on

(d

B)

Rd=1.5ohm

Rd=1ohm

Rd=0.5ohm

Isolation is maximum when the transmission line is exactly 90o and the effect of diodes similar to without transmission line when its length equalto 0o or 180o.

50

PIN diode switch(input impedance not 50

AC

V

Rs

Switch

50

Source

Load

4

Compensatingline

Compensating line is a 90o transmission line to match the Rs with 50ohm line.Rs is lower than 50 ohm.

50

All-shunt Diode Nonreflective SPST Switch

Input

D3D1 D2

D4

B1

Output

PIN diode switching operationSwitch Configuration

AC

V

50

50

Source

Load

Equivalent circuit

Diode "ON"(Switch "ON")

Diode "OFF"(Switch "OFF")

(Serial diode)

Isolation vs Diode capacity

0

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1

Diode capacity, Cd (pF)

Iso

lati

on

(d

B)

By putting diodes in series willreduce the total effective seriescapacity, thus increase isolation.This is shown in graph below.

PIN diode switching operation

Switch Configuration

AC

V

50 Switch

50

Source Load

50

4

In this case the optimum line line is not 90o, but depend onthe diode capacity.

Isolation vs Line length

0

10

20

30

40

50

60

70

0 50 100 150

Line length(deg)

Iso

lati

on

(d

B)

Single pole double throw PIN diode switches

/4/4

Output 1 Output2

Output 1 Ouput 2

Input

Input

Series

Shunt

Operation•One diode is biased in low impedance state with another diode in the high impedance state, so that input signal can be switched to one output to the other by reversing the diodes state or biasing.•The quarter-wave lines limit of the shunt circuit limit the bandwidth.

PIN diode application(TR switch)

TransmitterReceiver

dc supply Antenna

D1D2

dc blockdc block

Dc supply “ON” for transmitting. D1 and D2 will conduct,allowing the signal from transmitter to go to antenna andany signal go to receiver will be shorted. When dc supply“OFF”, D1 and D2 will not conduct, thus allowing only signal from antenna flow to the receiver.

PIN diode application(Reflective phase shifter)

RF input

RF output

A B

CD

90 o Hybrid

r2

Switched line phase shifter

2

1

in out

21

•Using two single pole and double throw switches to route the signal between one of two transmission lines of difference length. •The phase difference is . This circuit is a broadband & reciprocal phase shifter so that it can be used as receiver as well as transmitter.•Disadvantages-resonance when the length is multiple of /2 and frequency is shifted due to diode capacitance.

PIN diode application(8-steps phase shifter)

D2

D1

D2

D2

D1D1

RFC RFC RFC RFC RFC RFC

A B C

PIN diode application(8-steps phase shifter)

• When A, B or C is set “1” then D1 and D2 will conducted allowing the RF go straight.

• When A,B or C is set “0” then D1 and D2 will not conducted and the RF signal will experienced phase shift according to the length of U -line.

2 is 90o phase shift, /4 is 45o phase shift and 8 is 22.5o phase shift.

Switching equivalent phase shift

0 0 0 157.5o

0 0 1 135o

0 1 0 112.5o

0 1 1 90o

1 0 0 67.5o

1 0 1 45o

1 1 0 22.5o

1 1 1 0o

A B C Phase shift

PIN diode application Bridged T attenuator

D1 (R s1 )

D2 (R s2 )

Z o

RF input RF outputZ o

11log20

s

o

R

ZA 21

2sso RRZ where

Attenuation is small when D2 is forward biased (low impedance) and D1 is reverse biased (high impedance). Conversely , attenuation is large when D2 is reverse biased (high impedance) and D1 is forward biased (low impedance).

in

out

V

Va

Attenuation factor is defined as

PIN diode application attenuator

RF Input RF Output

D1 (R s1 )D2 (R s2 )

D3 (R s3 )

2

31log20s

s

R

RA

Attenuation is small when D3 is forward biased (low impedance) and D1and D2 are reverse biased (high impedance). Conversely , attenuation is large when D3 is reverse biased (high impedance) and D1 and D2 are forward biased (low impedance).

PIN diode application(intermodulation attenuator)

+20V

OUT 50/75

R2

R4

R5 R6

IN 50/75

R3R1

D1

D2

Vin=0-20V

R1, R2 2.2kR3, R4 1kR5, R6 75ohmD1, D2 UM9301unitrodeAll capacitors are 470pF ceramic

At high input voltage andlow attenuation, D1 tends toconduct signal.R1 and R2 set the current and isolatethe dc. D2 tends to be off.

At low input voltage and high attenuation, D1 tends tobe off. D2 tends to bypassthe signal to ground. R3 and R4 set the current and isolatethe dc. R5 and R6 maintainthe characteristic impedance

PIN diode application (intermodulation attenuator)

Input Voltage Vs Attenuation (dB)

0

10

20

0 5 10 15 20

Input Voltage (V)

Att

en

ua

tio

n (

dB

)

100MHz

200MHz

400MHz

Attenuation of signal after applying Vin for frequency 100MHz to 400MHz

PIN diode application (intermodulation attenuator)

Input Voltage Vs Return loss (dB)

10

15

20

25

0 5 10 15 20

Input Voltage (V)

Re

turn

lo

ss (

dB

)

100MHz

200MHz

400MHz

Return loss is less than 10 dB. It seem the impedance characteristic is maintain.

Attenuator

Input

Output

Coupler

Diode

Diode

Bias

Input

Output

Coupler Coupler

Diode

DiodeZ o

Z o

Bias

Attenuator (transmission mode)

Attenuator(Reflection mode)

Diode ON-attenuatedDiode OFF- transmitted