report analog circuit design ii

Character L circuit The impedance distribution circuit L has 4 forms as shown below: Figure 1.1: 4 types of impedance matching circuits L In which, there are two cases to consider: <

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Hanoi University of Science and Technology

School of Electrical and Electronics Engineering

REPORT

ANALOG CIRCUIT DESIGN II

Student: Do Nhat Hoang 20193219

Class: Advanced of Electronic Engineering K64 Instructor: Dr Nguyen Nam Phong

Hanoi, 03/2022

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Table of Contents

PART 1 CHARACTER L, PI AND T CIRCUITS DESIGN 3

1.1 Character L circuit 3

1.1.1: ( C ) Circuit 4

1.1.2 ( B) Circuit 5

1.1.3 ( D) Circuit 5

1.2 Pi Circuit 6

1.2.1 Low-pass Pi circuit: 7

1.2.1: High-pass Pi circuit: 8

1.3 Circuit of the letter T: 9

1.3.1 Low-pass T-circuit: 10

1.3.1 High-pass T-circuit: 11

PART 2 COMPARISON AND VALIDATION 12

2.1 Circuit classification 12

2.2 Advantage and disadvantage of each circuit 12

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PART 1 CHARACTER L, PI AND T CIRCUITS DESIGN

1.1 Character L circuit

The impedance distribution circuit L has 4 forms as shown below:

Figure 1.1: 4 types of impedance matching circuits L

In which, there are two cases to consider: < 𝑅𝐿 and > 𝑅𝐿 Down here is the circuit structure for the two cases, with is the series reactance, is parallel reactance:

Figure 1.2: Circuit structure with RS < RL

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Figure 1.3: Circuit structure with RS > RL

1.1.1: ( C ) Circuit

Consider a high-pass L circuit with RS < RL:

Figure 1.4: High-pass L circuit with RS < RL

Consider the circuit with series reactance C and parallel reactance L:

That

So that we have:

Also have:

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1.1.2 ( B) Circuit

Consider a low-pass L circuit with RS > RL:

Figure 1.5: Low-pass L circuit with RS > RL

Consider a circuit with series reactance L and parallel reactance C:

We have:

Performing the same transformation as circuit C, we get:

1.1.3 ( D) Circuit

Consider high-pass L circuit with RS > RL:

Figure 1.6: High-pass L circuit with RS > RL

We have:

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Similar to the case of circuit B, we have:

1.2 Pi Circuit

Figure 2.1: General Pi circuit

The Pi circuit can be described as two "opposed" L circuits, both of which are configurable to match the load and source with an invisible or “virtual” resistor located at the junction between the two networks

Figure 2.2: Pi circuit is equivalent to two opposing L circuits, with phantom

resistance in between

Q value of Pi circuit:

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From the result of circuit L, we have:

We also have:

From this we can determine the corresponding reactance values Pi circuits can be divided into two basic types: low-pass circuits and circuits high pass

1.2.1 Low-pass Pi circuit:

Figure 2.3: Low-pass Pi circuit

We have:

We also have:

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From that we can calculate the value of 𝑋𝐿, 𝑋𝐶1, 𝑋𝐶2

With : 𝑋𝐿 = 𝑋𝐿1 + 𝑋𝐿2

1.2.1: High-pass Pi circuit:

Figure 2.4: High-pass Pi circuit

We have:

We also have:

From that we can calculate the value of 𝑋C, 𝑋L1, 𝑋L2

With : 𝑋C = 𝑋C 1 + 𝑋C 2

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1.3 Circuit of the letter T:

Figure 3.2: General T circuit

Circuit T can be described as two series L circuits used to connect the load and source with a virtual resistor RV placed at the junction between two networks L RV must

be chosen greater than both and since it is connected connected to the shunt pin of each part of the L circuit

Figure 3.2: The T-circuit is the form of two L-circuits in series

The Q value of T circuit:

From the result of circuit L, we have:

We also have:

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From this we can determine the corresponding reactance values

T-circuits can be divided into two basic types: low-pass circuits and high-pass circuits

1.3.1 Low-pass T-circuit:

Figure 3.3: Low-pass T-circuit

We have:

We also have:

From that we can calculate the value of 𝑋C, 𝑋L1, 𝑋L2

With : 𝑋C = 𝑋C 1 // 𝑋C 2

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1.3.1 High-pass T-circuit:

Figure 3.4: High-pass T-circuit

We have:

We also have:

From that we can calculate the value of 𝑋L, 𝑋C1, 𝑋C2

With : 𝑋L = 𝑋L 1 // 𝑋L 2

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2.1 Circuit classification

Does not need to control

bandwidth

Need to control bandwidth

Q value gains from

calculation with given

reactance

Can choose the Q value Virtual resistance in

circuit Pi must be smaller resistance on the source and load

Virtual resistance in circuit T must be larger resistance on the source and load

2.2 Advantage and disadvantage of each circuit

in low pass filter

The circuit can change to L circuit by setting

a capacitor equal

to 0 Therefore it

is very flexible

- Good at high pass filter

- May be used for multi-band with the suitable value of L and C

bandwidth

- Hard to create

capacitor and inductor to work

at microwave frequency

- Require complex algorithm to design automatic impedance matching

- High cost due to having more components than L circuit

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References [1] Behzad Razavi (2011) RF Microelectronics, 2nd Edition, Pearson [2] Metin Şengül, Gökmen Yeşilyurt (2017) “Real frequency design of Pi and T matching networks with complex terminations”, 2017 10th International Conference on Electrical and Electronics Engineering (ELECO)

[3]A.R., A K., Singh, S G., & Dutta, A (2018) “Analytical design technique for real- -real single- and dual-frequency impedance to matching networks in lossy passive environment”, IET Microwaves, Antennas & Propagation, 12(6), 1013–1020

doi:10.1049/iet฀map.2017.078