TELECOMMUNICATIONS Dr Hugh Blanton ENTC 4307ENTC 5307 Impedance

TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

Impedance Matching • The power delivered to the variable load, RL is calculated by defining the output voltage first. Dr. Blanton - ENTC 4307 - Impedance Matching 2

• Then, the power delivered into RL is: Dr. Blanton - ENTC 4307 - Impedance Matching 3

• Plotting Pout versus RL shows that maximum power is dissipated in RL when it is equal to Rs. Dr. Blanton - ENTC 4307 - Impedance Matching 4

• RL = Rs is proved by differentiating P 0 UT with respect to RL and setting it equal to zero. Dr. Blanton - ENTC 4307 - Impedance Matching 5

• Power transfer is maximized when the source is “conjugate matched” to the load. • In case of resistive terminations, the source resistance must be equal to the load resistance for maximum power transfer. • High resistance load lead to high voltage but low current across the load. • Low resistance load result in high current but low voltage. Dr. Blanton - ENTC 4307 - Impedance Matching 6

• Real life terminations generally represent complex impedances, and their real parts may not be equal. • In such case, an impedance matching circuit is required to eliminate the mismatch. Dr. Blanton - ENTC 4307 - Impedance Matching 7

• For example, if Rs = RL = 50 W, and the load reactance (XL) is presented by a 1. 59 p. F series capacitors, the matching reactance must “negate” the load reactance. Dr. Blanton - ENTC 4307 - Impedance Matching 8

• At 100 MHz the necessary reactance is, Dr. Blanton - ENTC 4307 - Impedance Matching 9

• The bandwidth is determined by the Q of the circuit. Dr. Blanton - ENTC 4307 - Impedance Matching 10

• Perfect match (zero reflection coefficient) can only be achieved at selected single frequencies. • Matching a source to a complex load require two tasks: 1. The imaginary part of the load must be negated, or “tuned out. ” 2. The real parts must have equal values. Dr. Blanton - ENTC 4307 - Impedance Matching 11

• Small series parasitic capacitance or large series inductance leads to high-Q condition, leading to narrow-bandwidth frequency response. • If the reactive parts of the terminations are in different configuration (i. e. one parallel, one series) a series-to parallel conversion must be used before choosing the matching element. Dr. Blanton - ENTC 4307 - Impedance Matching 12

Matching Network Frequency Response • Analyzing the previously shown circuit verifies the computed 10 MHz 3 d. B bandwidth at the 100 MHz center frequency. • At the band edges the reflected energy |s 11|, and the transmitted energy, |s 21|, are exactly the same. Dr. Blanton - ENTC 4307 - Impedance Matching 13

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Impedance Matching Procedure Development • Recalling the series-parallel 1 GHz circuit equivalence, we now develop a generalized procedure to match two resistors at a given frequency. Note: RP>Rs Dr. Blanton - ENTC 4307 - Impedance Matching 15

• Using the above, match 50 W to 100 W. 1. 2. 4. 3. 5. Dr. Blanton - ENTC 4307 - Impedance Matching 16

• If the conversion is done by the above procedure, the series and parallel Q’s are equal. • If two uneven resistive terminations are to be matched, one can always be transformed by the above concept - to become identical to the other at a specified frequency. • By replacing one of the two reactive elements with its opposite type, conjugate match is established between the two circuits. Dr. Blanton - ENTC 4307 - Impedance Matching 17

• If the two terminations are real but have different values, they can be matched at any single frequency by an appropriate “L-Network, ” observing the following procedure: 1. Add a shunt reactance (capacitor or inductor) to the larger termination, such that 2. Add a series reactance. (opposite kind of what selected in step 1), to the smaller termination, such that Dr. Blanton - ENTC 4307 - Impedance Matching 18

• Compute the matching element values: Dr. Blanton - ENTC 4307 - Impedance Matching 19

• Using ideal matching elements, the insertion loss is zero at the center frequency. • Bandwidth depends on Q: • low Q results in wide bandwidth, • increasing Q decreases the bandwidth. Dr. Blanton - ENTC 4307 - Impedance Matching 20

• Design a circuit to match a 10 W source to a 50 W load at 400 MHz. Assume that the source and the load need to be DC-coupled, therefore use a lowpass circuit. Dr. Blanton - ENTC 4307 - Impedance Matching 21

Solution: • The need for a DC path between the source and the load dictates the need for an inductor in the series leg. • The Q is computed as: 10 W 50 W Dr. Blanton - ENTC 4307 - Impedance Matching 22

• Calculating the series and parallel reactances • Generally two component combinations exist: • lowpass or • highpass topologies. Dr. Blanton - ENTC 4307 - Impedance Matching 23

• The component values at 400 MHz are: • The final circuit with ideal components is: Dr. Blanton - ENTC 4307 - Impedance Matching 24

• Parasitic source inductance or load capacitance may be “absorbed” into the matching network: • Case I: Source with series inductance Dr. Blanton - ENTC 4307 - Impedance Matching 25

• Case II: Load with shunt capacitance: Dr. Blanton - ENTC 4307 - Impedance Matching 26

• Impedance matching takes place at 400 MHz only, and mismatch occurs at all other frequencies. • Of course, real physical circuits have frequency dependent dissipative losses that also affect the frequency response. • Absorbing the source or load parasitics into the matching network does not change the bandwidth of the frequency response. Dr. Blanton - ENTC 4307 - Impedance Matching 27

Impedance Matching - Complex Loads • There are two basic approaches in handling complex impedances 1. Absorption - Stray reactances are absorbed into the impedance-matching network, up to the maximums, that are equal to the matching component values. Dr. Blanton - ENTC 4307 - Impedance Matching 28

2. Resonance - Beyond the limits of maximum absorption, the excessive parasitics may be resonated with an equal and opposite reactance at the frequency of interest. • Once this is done, the matching network design can proceed for two pure resistances. Dr. Blanton - ENTC 4307 - Impedance Matching 29

• In the Resonance technique, LR resonates CM at the frequency of interest, leaving a resistive load. • For parasitic inductance, resonance is achieved by using a capacitor. Dr. Blanton - ENTC 4307 - Impedance Matching 30

• The resonating inductance (or capacitance when applicable): • Resonating a parasitic inductance or capacitance of a complex termination always leads to reduced bandwidth. Dr. Blanton - ENTC 4307 - Impedance Matching 31

Resonance Matching 1. Another approach is to fully resonate the parasitic portion first. 2. Then a suitable matching topology is selected with one component identical to the resonating element. Dr. Blanton - ENTC 4307 - Impedance Matching 32

• Finally, the matching and resonating elements are combined to save a component. • BUT, LR and 50 W define a Q equal to 20 p. F and 50 W. • Paralleling LR with CM will result in a higher loaded Q for certain. • Although this approach saves a component, the bandwidth is not quite as wide as it was in the previous case. Dr. Blanton - ENTC 4307 - Impedance Matching 33

Absorption Matching Network Example • A complex source of 50 W parallel with 5. 9 p. F capacitance is to be matched to a load of 10 W resistance in series with 3. 98 n. H inductance. • Design two matching networks (one lowpass and one highpass) on the Smith Chart, and compute the component values at 400 MHz (at that frequency the inductor represents XL = +j 10 W, x. L = j 0. 2 W. ) Dr. Blanton - ENTC 4307 - Impedance Matching 34

Absorption Matching Network Example In order to match impedances, we must create an reactance that negates the reactance of the load. z. L* Dr. Blanton - ENTC 4307 - Impedance Matching 35

• Lowpass solution: Selecting the shunt C-series L network: Dr. Blanton - ENTC 4307 - Impedance Matching 36

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ys z. L* y z Dr. Blanton - ENTC 4307 - Impedance Matching 38

• The highpass option may also be viewed as resonance matching since the 3. 98 n. H load inductance is resonated by part of the series capacitor Cs. • The 5. 9 p. F source capacitance is resonated by part of the parallel inductor LP. Dr. Blanton - ENTC 4307 - Impedance Matching 39

• Highpass solution: Selecting the shunt L-series C network: Dr. Blanton - ENTC 4307 - Impedance Matching 40

Absorption Matching Network Example In order to match impedances, we must create an reactance that negates the reactance of the load. z. L* Dr. Blanton - ENTC 4307 - Impedance Matching 41

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