From: Tom Bruhns on 27 Apr 2007 08:18:57 -0700
Yes, you are correct...caught me with a low level of caffeine on Thursday. :-)
Yes on the parallel L-C for the trap frequency. But, under low source impedance and high load impedance, with the approximate L and C given, there is a voltage increase at a frequency below the trap frequency. [there are four combinations of 3 components for L and C circuits, each with a peak versus dip impedance response, me has to keep reviewing those to avoid confusion] To explain, my (later) analysis model was as follows:
One-Ohm impedance current source. Parallel L-C in series with load, L1 = 10 uHy with Q of 150, C1 = 14 pFd. Load is 1 MOhm in parallel with C2, C2 varying 10, 20, 30 pFd. Capacitors were assumed essentially lossless since their typical Q at these frequencies can be 1000 or more. Minimum voltage response was at a nearly constant frequency regardless of C2 value. Maximum voltage response frequency varied considerably. Using 1.0 V RMS reference for 0 db, the response v. C2 value was:
C2 = 30 pFd, Vout peak +22 db at 7.8 MHz, Vout minimum -35 db. C2 = 20 pFd, Vout peak +26 db at 8.25 MHz, Vout minimum -32 db C2 = 10 pFd, Vout peak +21 db at 10.4 MHz, Vout minimum -26 db
I could have done the above with L1 Q of 50 but that would simply decrease the lower frequency peak voltage, show a lesser voltage minimum at the upper trap frequency, the rest about the same.
- At this point someone will get hot about "ya can't have voltage
- gain with no amplifier!" or equivalent. :-) Yes, one can since
- a voltage increase only means a current decrease at one
- frequency...the only power loss is in the Qs of the components.
Yes, but only for the series resonance frequency. There's a variation in the overall voltage response depending on the load resistance and its parallel load (and probe) capacity. For sure, a series-resonant circuit across the source is going to affect the gain of the driving source from its frequency variation of impedance.
This is one of those seemingly-inocuous circuit applications which can get very tricky to apply with any repeatability. Especially so when the source and load were unspecified. It's safe to say that EVERYTHING interacts over frequency and one cannot just assume anything. That includes scope probes which far too many apply thinking just of their
10 Meg input resistance and forgetting they all have capacity to ground in parallel. :-(Thanks for reminding me to go back to earlier basics, Tom. A number of years ago I worked the math on impedance of the four basic 3- component combinations and wrote it up for a work application (that would have been a high production failure situation if used as-is) and thought memory "would always be there." Actually it was but my mind gets cluttered with other stuff on a disorganized basis. :-)
BTW, I used my own LINEA (DOS-only) analysis program and LTSpice (free Windows compatible full package from Linear Technology) to run this simple circuit model. Results agreed.
73, Len AF6AY