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Figure 1-3 Click-to-talk application
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of the matching inductor. The same outcome can be attained by positioning a matching capacitor in parallel with any load or source XC, thus combining the two values into one larger value. This allows the internal stray reactances of both devices to actually contribute to the matching network, with these internal reactances now being subtracted from the calculated values of the LC matching components. In other words, the transistor s own stray reactances are now becoming an additive part of the matching network. This method is useful only if the stray internal reactances of the device are less than the calculated reactances required for a proper match, which is normally the case. The other technique is use resonance to resonate out the stray reactances of the device or circuit to be matched (at our desired frequency), with a reactance that is equal in value but opposite in sign, and then continuing as if the matching problem were a completely resistive one (R j0). This will make the internal stray reactances of the two devices or circuits disappear, thus allowing only the pure resistances to be easily dealt with. The first approach, absorption, is demonstrated with the practical example of Fig. 3.28a: 1. Disregard all source and/or load internal reactances. 2. Place an L network in series with the internal stray XL of the source, and the capacitance in parallel with the internal stray XC of the load (Fig. 3.28b). 3. While still neglecting all of the stray reactances, use the formulas and methods of resistive lumped L matching as outlined above to calculate and match RS to RL. 4. Subtract the internal stray reactance values from the L network s calculated values of L1 (2.5 nH) and C1 (3.58 pF), which in this case will be 2.5 nH 1 nH 1.5 nH L1 and 3.58 pF 1.5 pF 2.08 pF C1. 5. The new L network component values are now the actual values required to obtain the proper 12 j9.4 conjugate match for the 12 j9.4 source (or ZL 12 j0). To design a matching network employing the second method, the resonance approach, view the example circuit of Fig. 3.29: 1. Resonate out the 1.5 pF of stray capacitance within the load by employing a shunt inductor with a value of L 1 |2 f| CSTRAY
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YOU TRY IT Calculate ( d/dx) exp( x sin x) .
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Transmission Media Characteristics and Measurements 462 Basic Telecommunications Technologies
Project Milestones
14.0 110.3 26.6 150.9 19.4 150.0 225.0 110.0 53.2 708.6
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affect the plug number itself. The model then has to recalculate (or iterate) to adjust for this increase, which in turn will create another, but incrementally smaller, increase. The iteration will go through several more cycles before there is convergence within the limits set in the model. So, circular references can be used to good advantage. The dangerous thing is that as there is now a calculation loop in the model, if there is an error that gets inadvertently introduced into the calculations, this error message will continue to cycle around in the loop. Even after the source of the error has been removed, the error message continues to be caught in the loop! In this case, there are two ways to correct the situation: 1. Manually change one of the formulas so that the calculation loop is broken. Make sure that the source of the original error is corrected, and recalculate the model again to clear out the error message. Once this is done, restore the formula again. 2. A more elegant way is to use the ISERROR function to trap the error. Simply put, at a location in the calculation loop, we write a formula that returns a 0 when it encounters an error condition. Let s say we put this in cell C51: = IF ISERROR C50 ,0,C50 C50 is a cell that is part of the loop, as is C51. If there is an error in the loop, this formula in C50 will revert to a 0, which is then read by C51 and the rest of the calculations. The 0 breaks the circular loop and gives the error message a chance to be cleared out, so that when C50 calculates again, it does not see the error sign and automatically reconnects to C50. The loop is restored.
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