BÁO CÁO THÍ NGHIỆM KỸ THUẬT SIÊU CAO TẦN ppt

We will need to specify two of the parameters:  Z0, the characteristic impedance  TD, the time delay, which is the length of the line in time units.. The length of the line L is relate

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BÁO CÁO THÍ NGHIỆM

KỸ THUẬT SIÊU CAO TẦN

LAB 2: Basic Transmission Lines in the Frequency Domain

Student : Nguyễn Thị Bảo Trâm

Nguyễn Văn Hiếu

Đà Nẵng - 2010

In this laboratory experiment, you will use SPICE to study sinusoidal waves on losslesstransmission lines Our goal is for you to become familiar with the basic behavior of wavesreflecting from loads in transmission lines, and compare the simulations with numericcalculations and the Smith Chart

2.1 Basic Transmission Line Model

There is a standard lossless transmission line model T, which is specified by severalparameters We will need to specify two of the parameters:

 Z0, the characteristic impedance

 TD, the time delay, which is the length of the line in time units The

length of the line L is related to the time delay through

where up is the phase velocity of waves on the transmission line

As we saw in lecture and in our text, the phase velocity and characteristic impedance may bederived from the “lumped element” model of the transmission line With L’ the inductance perunit length, and C’ the capacitance per unit length, we have

up  1

(2.2)L'C'

- Inductance per meter ( H/m ) :

+ It is the series inductance per unit length, it appears from the shape of transmissionline Inductance per meter represents the self-inductance of the two conductors per a meter, italso represents the stored magnetic energy per a meter of transmission line

- Capacitance per meter ( F/m ) :

+ It is the shunt capacitance per unit length, it is due to the close proximity of the twoconductors, it also represents the stored electric energy per a meter of transmission line

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The inductance and capacitance per meter are:

We have: Z 

0

u p

L' 

 L' C'  L'  C'

Z 0 50 () ) ) 99L'

L'  u p 2

3



 250.108



 0,1.10  ()F/m)    0,1 ()nF/m)  3.108()m/s) 

For lossless coaxial cables, the following formulas relate the differential inductance L’ andcapacitance C’ to the radius of the inner conductor a and the outer conductor b:

L'   2 ln    b   a (2.4) C' 2

(2.5) 

()H/m) 4 2.36.1079

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Question 3: If b = 3 mm in question 2.2, what is a?

Answer: If b = 3mm in question 2.2 then:

a  4,235 b   3 ()mm)  4,235   0,708 ()mm) 

2.2 A SPICE model of a transmission line problem

Using SPICE, create a (matched) Thevenin source VAC with 1 Volt amplitude and 50 Ω source impedance, leading to a transmission line model T, terminated in a 100 Ω load Edit the transmission line so that it has a characteristic impedance of 50 Ω Also, create labels Input and Load at the ends of the transmission lines, so that you can measure the voltages conveniently

ZG

Input

50 1Vac

Question 4: At 200 MHz, and with up = 2/3 c, what is the wavelength in the transmission line?Answer: The wavelength in the transmission line is:

ߣ= ݌ݑ

݂ =

3ܿ 3×3.10 = 1(8 ݉) ݂ =200.10 = 50 Ω?

݉ /ݏ

6ݖ ܪݖQuestion 5: What is the time delay associated with λ/16?

(Hint: Remember that TD  L

up

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Figure 2 Illustration of Transmission Line Length Change for Part 2.2

One way to make this easier is to use a parameter for TD Place the special part PARAM Double click on it and then on New Column… Call it delay and set it to 5ns Assign {delay} (with the curly braces) to TD on the transmission line When you create your simulation profile, select the parametric sweep as an option Choose Global Parameter with a parameter of delay Set the sweep range and increment based on your TD calculations from above Under “General Settings” set the sweep Range from Start Frequency: 200Meg to End Frequency: 200Meg and increment Total Points: 1

Using Excel, make a table of the voltage magnitudes and current magnitudes at nodesInput and Load for each length

Question 6: Use PSPICE, Excel, or Matlab to plot the magnitude of the voltage at Input as afunction of length From the Voltage Values on the plot and the relationship: VSWR 

determine the VSWR, and from the VSWR calculate ||

Answer:

V max

V min

,

- To examine the change of input voltage as a function of length, we can examine thechange of input voltage as a function of Time Delay

We can simulate the input voltage as a function of Time Delay because Time Delay and Length

of transmission line relate together from the formular : TD L

 With up is a constant, L

u p 

increases n-fold as well as TD increases n-fold So, examining the change of the input voltage as

a function of TD is like doing this with L (length of transmission line)

 f  200.10 

So, we can establish a parameter in pspice with 0 at start value and 5ns at end value Inaddition, we examine L at the points which are λ/16-equidistant together Therefore, increment inparametric sweep is 0,3125ns like above value (question 5)

- Use PSPICE to plot the magnitude of the voltage at Input as a function of length:

720mV

(2.5000n,666.667m)

600mV

(1.2500n,333.333m) 400mV

- From the Voltage Values on the plot and the relationship: VSWR 

VSWR, and from the VSWR calculate ||:

ܸܹܴܵ =

݉

ܽ ݔ

666.667݉333.333݉ = 2

VSWR + 1 = 2+1=

3≈0.3333 The voltage and current yield the same VSWR and ||

Question 8: Plot the magnitude of the impedance at Input as a function of length using the data you collected with PSPICE Plot the Real and Imaginary Parts of the Impedance using

PSPICE and also plot impedance using a Smith Chart

Answer:

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- The magnitude of the impedance at Input as a function of length:

- Plot the Imaginary Part of the Impedance using PSPICE:

From the Smith Chart:

Yes, these answers agree with my previous answers: VSWR = 2 and || = 1/3

Question 10: Compute  and VSWR directly using equations (2.6) and (2.7) below Do theseagree with your measurements from question 6, 7 & 8?

From class recall that:

 Z L 9Z0

Z L  Z0

100 )50 ) 50  1 

   0.3333 

100 )50 ) 50  3 1

VSWR  1  Γ 

1 9Γ

1  

 19

3 

 2  1

3 These answers agree with my measurements from Questions 6, 7, and 8

Question 11: Plot the voltage magnitude at Load as a function of length How does the

voltage change with length? From this, how do you think the power delivered to the load willchange with length?

The magnitude of Load Voltage does not change with length

From this, I think the power delivered to the load will not change with length, too

- Plot the power at Load as a function of length:

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2.3 A shortcut, and more load impedances SPICE has a nice mechanism for scanning in frequency, but does not directly scan thelength of the transmission line The “electrical length” of a transmission line is βl,l,

Question 12: If you have 1 meter of the coaxial cable described in question 4, at what frequency does it have length λ/2? At what frequency does it have length 2.5λ? (Note that we are NOT changing the physical length of the line, only it’s “electrical length” as defined above.) Answer:

The coaxial cable in question 4 has frequency f = 200MHzThus it has length =

1ߣ at

2And it has length 2.5ߣ at

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Vmin

666.667mV 333.333 mV = 2

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Replace the 100 Ω load with a 25 Ω load

Question 14: Plot the magnitude of the voltage at Input, and compare to the previous case of

100 Ω From the plot, what is the VSWR? On a Smith Chart, what similarity is there between the

Replace the load with a “short circuit,” namely 0.001 Ω:

Γ  11

 50

⇒ VSWR= 1 9Γ =11 9 = ∞

These two results agree

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Replace the load with an “open circuit,” namely 1 MΩ (remember that in PSPICE, MEG =

These two results agree

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Question 17: How are the plots from Question 15 and Question 16 similar? How are these twoimpedances related on the Smith Chart?

L  ZL9Z 0

ZL Z 0

(2.9) Then you can project the load upstream through the transmission line to find the inputimpedance Zin

Zin

Z 0

150 L exp()2  jl) 

1  50 L exp()2 jl) (2.10) Now we can use the voltage divider at the source to find the voltage being applied to thetransmission line

g Z

in  Z g

Now, Vin is also the sum of the two waves so that we can write

Vin = V+ exp(-jβl,l) + V- exp(jβl,l) = V+ (exp(-jβl,l) + Γexp(jβl))exp(jβl,l)) (2.12)

So, putting this all together we have

3ܿ

1.65݉

= 8.25 × 10 =

−9 )ݏ݊( 8.25 = ݏ2

3×3.10

We have to set the TD to 8.25ns

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= 2 (݌

1 )݉/

1 = ߚ

ߚ ߚ 2

1+1 3.exp1−13.exp

(−2݆ × 3.3݌)

= 33.745 −݆ 24.068(Ω)(−2݆ × 3.3݌)

0.158

+ = ݃

= 1

ܼ ݉݅

݊+ܼ ݃33.745 +݆ 24.068 33.745 +݆ 24.068 + 50

(݆−ߚ)

exp ݆3.3݌

1 +

=

exp (−݆3.3݌)

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Question 19: Calculate Pav (average power delivered to the load), Piav and Prav (average power

in the incident and reflected waves, respectively) (Equations for Pav, Piav, and Prav are listed in Chapter 2 of the text.) Show that conservation of power been satisfied

 V  z   Z0I  z    V  exp   9 j z  (2.16)

 V  z 9Z  0I  z   V  9exp  jz  (2.17)V()z)  9Z0 I()z) 

V()z)   Z 0 I()z) L exp()2  jz) (2.18) Note that you can type equations into Probe in PSPICE to plot things like power, Γexp(jβl)), VSWR PSPICE can handle complex values Also note that the exp(jβl,z) parts in the above equationsaffect the phase only, not the magnitude Thus the above equations are ready to be input intoPSPICE, by setting the Voltage and Current values to the appropriate side of the transmissionline (Input or Load) By default, Probe plots the magnitude, but you can plot the real orimaginary parts, or the magnitude or phase by using the functions provided in the dialog boxthat comes up when you add a trace

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Question 20: Use SPICE to find the magnitude of V+ and V- at Input Use these values to compute Piav and Prav Do these match your answers in Questions 18 and 19?

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