TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

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

Dr. Blanton - ENTC Impedance Matching 3 Then, the power delivered into R L is:

Dr. Blanton - ENTC Impedance Matching 4 Plotting P out versus R L shows that maximum power is dissipated in R L when it is equal to R s.

Dr. Blanton - ENTC Impedance Matching 5 R L = R s is proved by differentiating P 0UT with respect to R L and setting it equal to zero.

Dr. Blanton - ENTC Impedance Matching 6 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 Impedance Matching 7 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 Impedance Matching 8 For example, if R s = R L = 50  and the load reactance (X L ) is presented by a 1.59 pF series capacitors, the matching reactance must “negate” the load reactance.

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

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

Dr. Blanton - ENTC Impedance Matching 11 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 Impedance Matching 12 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 Impedance Matching 13 Matching Network Frequency Response Analyzing the previously shown circuit verifies the computed 10MHz 3dB bandwidth at the 100MHz center frequency. At the band edges the reflected energy |s 11 |, and the transmitted energy, |s 21 |, are exactly the same.

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Dr. Blanton - ENTC Impedance Matching 15 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: R P >R s

Dr. Blanton - ENTC Impedance Matching 16 Using the above, match 50  to 100 

Dr. Blanton - ENTC Impedance Matching 17 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 Impedance Matching 18 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 Impedance Matching 19 Compute the matching element values:

Dr. Blanton - ENTC Impedance Matching 20 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 Impedance Matching 21 Design a circuit to match a 10  source to a 50  load at 400MHz. Assume that the source and the load need to be DC-coupled, therefore use a lowpass circuit.

Dr. Blanton - ENTC Impedance Matching 22 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:  

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

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

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

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

Dr. Blanton - ENTC Impedance Matching 27 Impedance matching takes place at 400MHz 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 Impedance Matching 28 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 Impedance Matching 29 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 Impedance Matching 30 In the Resonance technique, L R resonates C M at the frequency of interest, leaving a resistive load. For parasitic inductance, resonance is achieved by using a capacitor.

Dr. Blanton - ENTC Impedance Matching 31 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 Impedance Matching 32 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 Impedance Matching 33 Finally, the matching and resonating elements are combined to save a component. BUT, L R and 50  define a Q equal to 20 pF and 50 . Paralleling L R with C M 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 Impedance Matching 34 Absorption Matching Network Example A complex source of  parallel with 5.9pF capacitance is to be matched to a load of  resistance in series with 3.98nH inductance. Design two matching networks (one lowpass and one highpass) on the Smith Chart, and compute the component values at 400MHz (at that frequency the inductor represents X L = +j10 , x L = j0.2 .)

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

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

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Dr. Blanton - ENTC Impedance Matching 38 zLzL zL*zL* ysys y z

Dr. Blanton - ENTC Impedance Matching 39 The highpass option may also be viewed as resonance matching since the 3.98nH load inductance is resonated by part of the series capacitor C s. The 5.9pF source capacitance is resonated by part of the parallel inductor L P.

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

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

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