Input Capacitor
Viewing the circuit in the above chart, you can see Esig, which is the input signal for the circuit. There is initially a capacitor in the circuit for the purpose of coupling the signal to a prior stage or instrument. In case this has not been mentioned previously, the purpose of a capacitor in this position is two-fold:
1) Block the DC voltage from a prior stage
2) Pass the AC signal to the amplification stage
Input Resistor
So the signal travels from a source (such as a guitar or record player) through this capacitor. The next thing in the chain is the input resistor Rg1. The basic requirement for this resistor is that it be large enough to dominate the voltage divider formed by the source impedance. As you can see, we can choose any value in the 3rd column for this resistor, ranging from .1 to 10 MOhms. Following the example on Boozhound, I am choosing 100k. This is a pretty typical value for a record or guitar amplifier. Now the voltage across Rg1 is our input signal, which exists at the grid of the 6SN7.
Load Resistor
The next decision we must make is based on what we will be driving with this tube. Again, following the Boozhound example, we will be driving the input to a subsequent stage of the circuit. In this case, we are driving a 240kOhm resistance. So far we have
Rg1 = 100k
Rs = 240k
Therefore we direct our attention to the only row where Rg1 and Rs have these values (row 2). Here you can see we have a few options as far as the plate voltage goes: 90V, 180V, and 300V. You can see by comparing the columns for Eo at each voltage that the plate voltage determines how much output the amplifier can drive. For instance, looking at the row we have chosen to work with based on the input and load resistance (again, row 2), if Ebb=90V, the maximum output from this amplification stage is 16 volts RMS before the onset of distortion. Increasing Ebb to 180V allows the tube to produce 33 Vrms before the onset of distortion. I have chosen 180V. After decisions for input resistance, output load, and plate voltage are made, you pretty much just need to match the values to the parts in the schematics and simulate. I have made this file for LTSpice and stored it here. A drawing of the file is here:
Accuracy of Simulation Compared to Data Sheet
According to the first table, we expect the amplifier to have a voltage gain of 15 with the onset of distortion occurring when the amplifier tries to produce a signal with an RMS value of 33V. Using an input signal of 1V for normalization, we can get the following plot to test the transfer function of the equation:
Reading this plot, you can see that the gain is approximately 24 dB. “Argh,” I hear you moan in response to having to compare dB to a simple multiplicative gain. Honestly, I completely agree with you—this is annoying. However, decibels are nice for describing amplification because numbers like 1500X as loud start sounding a little silly. And even though this stage is only 15X the original signal, it will be fed into another stage that will multiply that signal by more, so the overall gain gets out of hand pretty quick. Back to the question at hand of whether the simulation is accurate, we must answer whether 24 dB gain is the same as 15X the original signal. The equation for the output gain in dB is
# dB = 20 * log(Vout/Vin)
Solving for dB, using Vout/Vin = 15 yields 10^1.2, which is approximately 15.8. Therefore, the simulation is pretty true to the data sheet. While we’re at it, I think it would be instructive to discuss the onset of distortion. Distortion is an important topic for both Hi-Fi tube amplifiers and guitar amplifiers, since you generally want to avoid distortion in the former and sometimes you want to create it in the latter. Viewing the data sheet you can see that the amplifier will experience 5% harmonic distortion when trying to create an output with an RMS-voltage of 33V. This time, I will use the transient response capabilities of LTSpice to simulate the scenario where the amplification creates a 33V output signal. I will use a 1 kHz signal for the simulation. From the frequency response, you can see the 1 kHz signal will be amplified by about 22 dB (12.6X the original signal using the above equation). Using the gain and definition of RMS voltage, you can find that a voltage of 3.6V will cause the gain stage to try to drive approximately 33V RMS, thereby introducing 5% harmonic distortion. This is shown below.
You can see a small amount of asymmetry in the negative cycles of the waveform, but this looks pretty nice, so presumably 5% harmonic distortion, although probably not an acceptable parameter for audiophiles with good ears, is not visible to the eye at least. To test if we are near a threshold point, I am running the simulation again with a 6V input signal at 1 kHz (shown below):
Here you can see the characteristic onset of distortion in the negative cycle of the waveform. This is all pretty cool, if I do say so myself, since it seems the simulation and data sheet match fairly well.
Cathode Bypass Gain Switch
I will do an analysis a bit later regarding how this sounds, but for now, I would like to discuss a simple method of adding a gain switch to this preamp stage. This method of adding gain is very simple. All I am going to do is add a switch to the cathode capacitor (Capacitor C1 in the circuit). The tube’s amplification abilities are related to the voltage at the cathode. There is always an AC signal at the cathode related to the input signal due to the nature of the tube. The role of C1, called the cathode bypass capacitor, is to filter this signal so that the node at the cathode is mostly zero. Removal of this capacitor allows the AC signal to exist at the cathode, thereby creating fluctuations in the cathode voltage. These fluctuations result in a reduced gain. The frequency response of the amp without the capacitor is shown below:
Wow! We have reduced the gain from 24 dB to 19 dB. You will also note that this capacitor was acting as a HP filter when in the circuit, since the low frequency response is much more flat. Two things can be learned from this: 1) you can put a switch to connect or disconnect the capacitor C1 to create a +5 dB gain stage and 2) if you want to maintain a flat frequency response, you should be careful in choosing your cathode bypass capacitors, since they are HP filters.
I will wax philosophical for a moment here and would love any input from more experienced builders regarding the topic of cathode bypass. From the above analysis, it seems like this is one place where the goals of a guitar amplifier and Hi-Fi amp might be at odds. Generally, it seems like Hi-Fi amps would want to avoid bypass caps as much as possible to maintain signal fidelity, while guitar amplifiers might want to use the capacitors to achieve higher gain, earlier onset of preamp distortion, etc.. Any thoughts?
Okay amp lovers. Today we have learned
1) How to pick parts for building a cathode-biased preamplifier stage using the data sheet for a 6SN7 tube
2) How to simulate said circuit in LTSpice
3) Made comparisons between data sheet and simulation for amplification parameters and distortion onset
4) Discussed the use of cathode bypass capacitors as a gain switch
That is all for now. Now, go huff some solder fumes, grill some bratwurst, have a beer, or go biking. Personally, I am gonna do all four.
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