Microwave Ring Circuits and Related Structures phần 4 ppt

proposed.The equivalent circuit given in Figure 4.5 can also be used for diodes

other than varactors. The only difference will be the value of the parameters.

In Figure 4.5 Cj is obviously the capacitance that arises from the semicon￾ductor junction. It is this value in which we are most interested; all the others

are undesirable but unavoidable. The value Rs is the series resistance due

primarily to the bulk resistance of the semiconductor. Minimizing Rs increases

the Q of the varactor (here, Q = 1/wRsCj), reducing power losses in the circuit

and increasing the overall circuit Q. Typically higher Q-values are obtainable

with hyperabrupt junction varactors because of the lower bulk resistance.

The parameters Cp, Lp, and Ls are the parasitics introduced by the package.

The capacitance Cp, which appears in shunt, is a combination of the capaci￾tance that exists between the upper contact and the metallic mount of the

semiconductor and the insulating housing. Because of the close spacing

required in microwave frequency circuits, particularly for small elements that

102 ELECTRONICALLY TUNABLE RING RESONATORS

FIGURE 4.4 Diagram of a varactor package cross section.

FIGURE 4.5 Equivalent circuit of a packaged varactor.

possess small junction capacitances, the capacitance contribution can become

quite significant. The capacitance C2 is also included in Figure 4.5. Here C2 is

the capacitance that arises from the gap in the transmission line across which

the diode will be mounted. This is the same gap capacitance discussed in

Chapter 2. The gap shunt capacitance, C1, is omitted because its effects are

considered to be negligible.

In addition to the capacitances, all metallic portions of the package will

introduce inductance. The inductance is divided into two components Ls and

Lp.The inductance Lp appears in series with the junction capacitance.The most

significant contributions of the inductance come from the metallic contacting

strap and the post upon which the semiconductor element is mounted. The

contributions are significant because of the very small cross-sectional dimen￾sions of the parts with lengths that are comparable to the dimensions of the

package. The inductance Ls represents the series inductance of the outer end

parts to the external contacting points.This can become very large if long leads

are required for bonding to the circuit.

The equivalent circuit does to some extent actually represent the physical

contributions of the typical packaged diode structure and can be useful over

a wide range of frequencies. Values for the equivalent circuit will vary for each

diode type and package style. Because the packaged-diode equivalent circuit

is widely recognized, manufacturers usually supply typical parameter values

for each package style and diode type.

4.4 INPUT IMPEDANCE AND FREQUENCY RESPONSE OF THE

VARACTOR-TUNED MICROSTRIP RING CIRCUIT

Now that the equivalent circuit for the varactor has been proposed, the input

impedance of the circuit can be determined [1, 3]. In Chapter 2 it was verified

that the transmission-line method could be used to accurately determine the

resonant frequency of the microstrip ring resonator. The equivalent circuit of

Figure 2.12 should then adequately represent the ring and coupling gaps. The

varactor-tuned ring will differ only slightly from the plain ring resonator.

To mount the varactor in the circuit, the ring will be cut at two points and

the varactor placed across one of the cuts, while a dc block capacitor is

mounted across the other cut. The dc block capacitor is chosen to have a large

value. The capacitor is required so that a dc bias voltage can be applied across

the cathode and anode of the varactor. At microwave frequencies the capac￾itance will appear as a short and have very little effect. For low frequency,

however, the capacitance appears as an open circuit and allows the varactor

to be biased. To apply the voltage to the device, bias lines connect to the ring.

The bias lines are high impedance lines. The bias lines act as RF chokes, pre￾venting the leakage of RF power, while at the same time allowing the applied

dc bias voltage to appear across the terminals of the device. The layout for the

varactor-tuned ring is given in Figure 4.6.

INPUT IMPEDANCE AND FREQUENCY RESPONSE 103

Because Figure 2.12 has proved to be accurate, we will modify it to repre￾sent the varactor-tuned ring. The only changes made to the ring are the intro￾duction of the varactor, dc block capacitor, bias lines, and gaps cut in the ring.

If the bias lines are designed with a high enough impedance, they should have

little effect on the circuit and will be neglected in the analysis. The proposed

equivalent circuit for the varactor-tuned ring is given in Figure 4.7.The param￾eters C1 and C2 are discussed in Chapter 2 and are used to model the input and

output coupling gaps. The parameters Za and Zb are from the T-model for the

transmission line of the ring, also discussed in Chapter 2. The impedance Zbot

represents the bypass capacitor. Because the bypass capacitor wilt be large

(usually 10 pF or larger), the capacitance of the gap across which the dc block

is mounted can be neglected. In fact, because the bypass capacitor is large, it

acts as a very low impedance (short circuit) at microwave frequencies. Thus,

for this application the dc block capacitor could be neglected, but it can be

104 ELECTRONICALLY TUNABLE RING RESONATORS

FIGURE 4.6 Diagram of varactor-tuned ring resonator [3]. (Permission from IEEE.)

FIGURE 4.7 Equivalent circuit of a varactor-tuned ring [3]. (Permistion from IEEE.)

included to make the input impedance equations more flexible for other appli￾cations. The impedance Ztop represents the varactor mounted in the ring. The

equivalent circuit for the varactor was given in Figure 4.5.

The load seen by the ring at the output coupling gap is given as ZL¢ where

(4.5)

and A and B are defined in Chapter 2. The ring structure is not symmetrical

and therefore cannot be reduced through combinations of series and parallel

impedances. A unit voltage is applied to the circuit and six loop currents are

visualized. From the six loop currents, a system of six equations and six

unknowns is formed. The input impedance looking into the gap, Z¢, can be cal￾culated by solving the sixth-order system of equations for the currents due to

a unit source. The system to be solved is

(4.6)

where

and

Once the currents are known, then

Z =

+ -

- ++ -

- + +¢ ¢

¢ + +¢ -

- ++ -

- +

Ê

Ë

Á

Á

Á

Á

Á

Á

Á

ˆ

¯

˜

˜

˜

˜

˜

˜

ZZ Z

Z Z ZZ Z

Z ZZZ Z

Z ZZZ Z

Z Z ZZ Z

Z ZZ

ab b

b ab b

b abL L

L abL b

b ab b

b ab

0 0 00

22 0 0 0

0 00

00 0

0 0 0 22

00 0 0

bot

top ˜

I =

Ê

Ë

Á

Á

Á

Á

Á

Á

Á

ˆ

¯

˜

˜

˜

˜

˜

˜

˜

i

i

i

i

i

i

1

2

3

4

5

6

V =

Ê

Ë

Á

Á

Á

Á

Á

Á

Á

ˆ

¯

˜

˜

˜

˜

˜

˜

˜

V

V

unit

unit

0

0

0

0

V IZ =

Z A jB L¢= +

INPUT IMPEDANCE AND FREQUENCY RESPONSE 105