“The Electronics Of Radio” NorCal 40B Transceiver Build Lab Notes: Problem 3
This continues a series of blog posts on David Rutledge’s text, “The Electronics of Radio”, that I am studying while building the NorCal 40B transceiver. This series of posts will not be a review of the book, nor is it a assembly manual. Rutledge presents a series of problems at the each chapter that aid in understanding electronics and building the 40M QRP CW transceiver. I am going to try to go through all of these problems and document them here. All of these are titled similarly, so search for them that way. For what its worth, most people will want to skip these posts, they are really for my own self-education on electronics and may not make a lot of sense unless you have Rutledge’s book.
Here is the circuit. I went ahead and soldered the two components together to make it easier. Otherwise, this is specifically how the book specified the connections to be (i.e., no breadboard introducing stray electrical phenomena).
This next part, C & D, is problematic, and I spent a lot of time working this out. When I worked my way through this, I was stuck on the fact that my “t2” time measured very similarly to my calculated time constant τ. Specifically, t2 was designated as the amount of time that the RC circuit took to discharge to 0 volts. The waveform drawn below is a modification of a 20Hz 1Vpp signal from a function generator through the assigned RC circuit, which after encountering the 1MΩ impedance, has an actual measured amplitude of 1.56Vpp.
Specifically, my oscilloscope is an old model which does not superimpose a “zero voltage” line onto the detected waveform. In order to follow the book’s instructions to find the “zero voltage” line and measure the amount of time from the falling edge of the waveform until it reaches zero volts, I needed to change the coupling to GND, and then mark the zero voltage on the scope. As shown below, the voltage drop from the falling edge of the waveform to the zero voltage line is approximately 0.97 volts.
As shown below, it takes around 2.3 ms from the start of the falling edge of the signal crosses the zero voltage line. Note, I measured these several times, so there may be slight discrepancies between the pictures I took and what I finally thought were the best values to record.
Now, part “D” is where I ran into problems. I needed to calculate t2 form the Rth (also called Rs) and the 10nF load capacitance. And it was this from the book that screwed me up: “When the voltage drops to zero volts, the capacitor has discharged halfway. The time for it to reach 0V is the time t2 that we related to the time constant τ.”
Well, what this statement meant to me was that t2 was the half-life of the capacitor charge, a value given by 0.693 * τ. The time constant τ = R * C, which is 2.48ms. Multiplying τ by 0.693 would be 1.72ms, obviously a much smaller relative amount of time compared to the t2 I measured (2.32ms). Obviously this was not correct. But I was having trouble identifying the problem.
Then! I realized that in my mind, since I was injecting a 1Vpp signal into the circuit (which would be an open circuit voltage of 2Vpp) and that I was measuring nearly 1V between the start of the falling edge of the signal and the zero voltage line, that it meant I was discharging the capacitor to 50% by the time it reached 0 volts. In fairness, this was indeed what the book stated. But this is not correct. The amplitude of the signal is 1.56V. So in reality, the t2 time is the discharging of 0.97V of that 1.56V, or 62.2% (measured). Which is awfully close to 63.2% discharge of the initial starting voltage of the capacitor, which whatever time that it takes to discharge a capacitor 63.2% is its time constant by definition. The answer to this problem is that the calculated time constant τ is equal to the measured t2 on the oscilloscope…whew, this one took a bit to sort out. And honestly, I am not entirely sure I have sorted it out…
Part E proved to be a problem too. The point was to remove the capacitor, and then show that there was still enough capacitance to have non-vertical rise and fall times of the square wave. But as you can see, my CRT scope shows the resistor-only circuit as a perfect square wave, without visible vertical lines. (Time for a digital scope??!) When I looked at the notes though, the author recommended a Tektronix 2215A, which is an analog scope as well, so I am not sure why he can see vertical lines, but I can’t. Regardless, in order to get the most out of this portion of the book, I am going to assume t2 for this circuit is ten times what it would be with the capacitor (10 x 2.32ms = 23.2ms).
Although as I kept on going through this section, I realized I could directly measure the capacitance of the probe with my PEAK LCR45 meter. I chose to attach the the leads of the LCR meter to the center pin of the o-scope probe and the BNC center pin while the probe was in 10x mode. The capacitance of the probe, Cp, measured 17.9 pF. The ProbeMaster 4902 Switched 1X/R/10X probes have a published capacitance of 14pF in 10x mode. I’ll use 17.9pF for the remaining calculations of Cp in this problem set.
This photo shows the oscilloscope capacitance (Co) of 15pF.
I went ahead and tried part J, but the instructions were for the previously described single resistor circuit (I think, its a bit unclear). I built it with the original RC circuit instead because at least I would be able to see the vertical CRT phosphors lighting up. Regardless, I could not correctly calculate T2 for this circuit (which is the time it takes the capacitor to discharge to the zero voltage point). Below, the measured T2 is 2.847ms. And unlike the 1x probe, it appears that the the zero crossing does occur midway between the entire peak to peak amplitude (i.e., with 1 volt above the zero crossing and 1 volt below, see second pic down). The zero crossing is set at the horizontal line with vertical markings.
Below is a photo showing the square wave from the signal generator through the original RC circuit, showing a Vpp of 2.09V. But if you look carefully, you can see that channel one’s volts/div is actually 50mV/div, which would add to only about 200mV/div. My o-scope compensates for this automatically and multiplies the voltage by 10 when using the high impedance probe function, thus showing the 2.09V total. Without the automatic compensation, the o-scope measurement is approximately the same as what I calculated in part K.
I am going to hang up problem 3 now. While my circuit analysis and math may be a part of the issue with my results, I have to say that my decades old lab equipment was also tripping me up. For instance, I am actively on the lookout for a new function generator. One, I need AM (and want other) signal modulation capabilities in order to do some of the problem sets in this book. Two, my function generator does not display its amplitude! In fact, the voltage knob is also the on-off switch, so I cannot turn off the generator without having to reset the voltage. Which means I actually have to test the voltage output with a separate instrument because, like I said, there is know output voltage display. This is definitely problematic because in order to check the voltage, I need to break off the signal from my circuit and test it. I also actually found the10x automatic compensation of my scope to be a bit confusing while working through these problems. But, when not manually calculating circuits, it is nice to have the scope automatically correct its voltage when the high impedance setting on the probe is used. I am starting to wonder if the impressive functionality of a modern digital scope may be worth it though; there is a lot of guessing with an analog scope (if only my instrument rack had more space…)
I am only on chapter 2 of “The Electronics of Radio” and there are still problems 4, 5, and 6 left. Unfortunately, until I upgrade my signal generator, I will not be able to complete problem 4. Today, I also received the NorCal 40B transceiver kit. The first components to be soldered on the radio’s PCB occur in problem 8.
Well, that is it for now. It is late.
Mindy