Lecture 6: Parallel Resonance and Quality Factor. Transmit Filter.

Transcription

1 Whites, EE 3 Lecture 6 Page 1 of 10 Lecture 6: Parallel esonance and Quality Factor. Transmit Filter. As we saw in the last lecture, in order for a series LC circuit to possess a large Q the reactance of L or C (at resonance) must be much larger than the resistance: 0L 1 Qs (3.90) 0C Consequently, if we desire a large Q (very good frequency selectivity) in a series tank circuit, the resistance should be relatively small (for a reasonable X). For example, a resistance of is common for receivers and some antennas. This relatively small resistance is seen by the F Filter in the NorCal 40A, which uses a series LC filter. Parallel esonance However, if the load resistance in the circuit is relatively large, it becomes more difficult to achieve the high reactances at resonance necessary for a highq series LC circuit. If this is the case and it often is in the NorCal 40A then a designer needs to use a parallel resonant LC circuit (Fig. 3.7): 016 Keith W. Whites

2 Whites, EE 3 Lecture 6 Page of 10 I L C V For this parallel LC circuit Q p which is the inverse of Q s. resistance reactance 0 Following the analysis in the text (Section 3.7), we find that the frequency response is similar to a series LC circuit V V i V i f f l f 0 f u f esonant frequency defined as the f where reactance X = 0. However, Qp 0C 0L (3.109) For a highq parallel resonant circuit, we need a small reactance of L or C (at resonance) compared to the resistance. Sometimes this is easier to do when is large in a parallel LC circuit than with a high reactance in a series LC circuit.

3 Whites, EE 3 Lecture 6 Page 3 of 10 Examples: () 7.00E06 = resonant frequency 15 = Qp = Qs = Q Series LC Parallel LC Check: Ls=Q/0 Cs=1/(0Q) Lp=/(0Q) Cp=Q/(0) f0,s=1/(sqrt[lscs]) f0,p=1/(sqrt[lpcp]) E E E08 6.8E E E E E1 7.58E07 6.8E E E E E1.7E06.7E E E E E E E E E06 The green highlighted case is close to the F Filter in the NorCal 40A (series LC). 7.00E06 = resonant frequency 100 = Qp = Qs = Q Series LC Parallel LC Check: () Ls=Q/0 Cs=1/(0Q) Lp=/(0Q) Cp=Q/(0) f0,s=1/(sqrt[lscs]) f0,p=1/(sqrt[lpcp]) E E1 1.14E E E E E E E E E E E03 1.5E E07 1.5E E E E E14 6.8E E E E06 Three things we can observe from these examples: 1. For higher Q in a series LC (at fixed ) we need to use a larger L or a smaller C (larger reactance for L and C).. For higher Q in a parallel LC (at fixed ) we need to use a smaller L or a larger C (smaller reactance for L and C). 3. For a fixed, smaller L and larger C (smaller reactance for both L and C) are needed in a parallel LC circuit to achieve the same Q as a series LC. Also, as mentioned in the text,

4 Whites, EE 3 Lecture 6 Page 4 of 10 f Q f which is the same expression as for Q s. 0 p (3.110) A number of parallel LC circuits are used in the NorCal 40A. One of these is the Transmit Filter constructed in Prob. 9. Transmit Filter The Transmit Filter is a modified parallel LC circuit (see inside front cover). The Transmit Filter is mainly used to filter all harmonics other than 7 MHz coming from the Transmit Mixer (see Fig. 1.13): C37 5pF V in C38 100pF C39 50pF L6 3.1H V out This is not a true parallel LC circuit in the sense of Fig. 3.7a. It is important to analyze this circuit for use in Prob. 9. First, we ll combine C38 and C39 and include losses from L6:

5 Whites, EE 3 Lecture 6 Page 5 of 10 C c Norton Equivalent V in C'= C38C39 L6 Vout We ll use a Norton equivalent circuit for V in and C c : Vin 1 Isc jcv 1 c in and ZTh jc jc Using this in the previous circuit: c c I in = C c C' V out jc c V in L which we can reduce to I in C V out L This is still not a parallel LC form. Instead, this is called an LparallelC (L C) circuit. The characteristics of this

6 Whites, EE 3 Lecture 6 Page 6 of 10 circuit (and the C L) are listed at the end of this lecture (from Krauss, et al. Solid State adio Engineering ). Here are those characteristics of the L C circuit important to us right now: Quantity 0 Q t Approximate Exact Expression Expression (Q t >10) 1/ 1 1 LC L LC 0L 1 0C t 0C L Qt Qt 1 C C Q t 0LQt t 0 What is particularly relevant here are the approximate expressions for large Q t. These are precisely the same equations for a standard LC circuit, but with an t : I in C L t V out t is not an actual resistor but rather an effective resistance. This t is quite large in the Transmit Filter. Let s check some numbers for the NorCal 40A:

7 Whites, EE 3 Lecture 6 Page 7 of 10 C C c C38 C pf, L L H, L 0L 0 0L6 t t Q L6 What is the resistance of L6 at 7 MHz? Not as obvious as it looks. (Due to the skin effect, the resistance of wire changes with frequency.) Let s assume L6 1. Then, 0L6 t k L6 Whoa! That s big. The Q of this L C Transmit Filter should then be t Qt 18, That s a respectable Q for a discreteelement LC circuit. Your measured value will probably be less than this (more losses). Summary The Transmit Filter shown on p. 4 of this lecture can be modeled by an effective parallel LC circuit shown on the previous page. It is emphasized that t is not an actual resistor, but rather an effective resistance due to losses in L6 and other effects mentioned in Prob. 9. You can use the analysis shown here to help with your solution and measurements in Prob. 9.

8 Whites, EE 3 Lecture 6 Page 8 of 10 Lastly, you will find through measurements that this modified parallel LC circuit has a much larger Q than if C37 were removed (yielding just a regular parallel LC tank). Interesting! Winding Inductors and Soldering Magnet Wire You will wind the inductor L6 that is used in the Transmit Filter. It is specified in the circuit schematic to be constructed from 8 turns of wire on a T37 core, which is a toroid of 0.37in diameter constructed from a #mix iron powder. It is important you develop the habit of winding the toroids as illustrated in the text and in the NorCal40A Assembly Manual tutorial. Hold the toroid in your left hand and begin threading the wire through the top center of the toroid with your right hand. Each time the wire passes through the center of the toroid is considered one turn. You ll need a small piece of fine sandpaper to clean the varnish off the ends of the magnet wire before soldering. Not removing ALL of the varnish will likely cause big problems because of

9 Whites, EE 3 Lecture 6 Page 9 of 10 poor ohmic contact. I check the continuity between the solder pad and a portion of the magnet wire sticking up through the solder meniscus to confirm good ohmic contact.

10 Whites, EE 3 Lecture 6 Page 10 of 10 (From H. L. Krauss, C. W. Bostian and F. H. aab, Solid State adio Engineering. New York: John Wiley & Sons, 1980.)