Hardwiring, Layout Problems | Solutions To These Problems | Interstage Signal Feedback Through the Power Supply | Resistor comparisons
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Thank you for checking out this paper on power supplies and capacitors. At the outset, I MUST mention that this article is a compromise between being technical and being easily understood. This involves clarity, simplicity, with the mathematics left out. (Engineers will know the mathematics and accurate formula and be able to more precisely fill in the blanks, so to speak.) I have therefore taken the necessary liberties to write as simply and clearly as possible. I simply want the general audience to get the overall concept that in the power supply, types and quality of capacitors do make a difference. By the way, this subject was partially covered some 55 years ago in the RCA Radiotron Designers Handbook, in 1980 by Walter Jung/Richard Marsh, and in 2015 by Audio Engineering Associates . So the problems discussed here have been addressed over the decades.
Surfing the internet, I have seen many articles concerning audio designs, tube and transistor. However, the power supply is one of the few regions not intensively investigated, understood, or at least written about. It is also a weak link in any audio component. There are several areas to consider when designing a power supply.
There are plenty of articles addressing the first two points. However, I have yet to see an article that addresses the third point. In fact, many assume that a simple "de-coupling" capacitor addresses the problem entirely. It does not, as we shall see. In my example below, C1 is the decoupling capacitor.
We understand that a vacuum tube, or a solid state device, has resistance, and current flow, and requires a DC voltage in order to work. The power supply "filter" decoupling capacitor, C1, in series with R1 form a musical signal current path to ground. Simple ohm's law, I = E/R proves such, just as it does with musical signal current "flows" through coupling capacitor C2 and the following grid resistor to ground. C1s purpose is to provide a stable voltage gain environment below and above all audio frequencies.
Let's take a look at a typical audio circuit (fig.1) and its' A.C. "equivalent circuit" (fig.2) if the capacitors were perfect.
Now notice that in (Fig. 2), the symbols for capacitors C1 and C2 (perfect capacitors) are missing; with a line drawn to ground for C1, and straight wire output for C2 (we are only concerned with AC, not DC.). In other words, the top of R1 is perfectly grounded for all AC musical signal frequencies and beyond. The Thevenin model of fig. 1, 2 appears below.
Notice C1 has a line through it. C2 is also a line. The only purpose of showing C1 is that it is necessary because of a DC voltage being necessary/present. However, C1 presents some problems.
In the real world, C1 is not zero impedance due to its finite ufd size and internal construction, which includes internal DC resistance and inductance. So how does imperfect C1 influence a circuit at different frequencies, in otherwards the music?
The equation for capacitive reactance (AC resistance) is Xc = 1/ 2pi times Frequency times Capacitance in ufd. C = 1/2pi X F X C in ufd. A capacitor's AC resistance should vary with frequency. But due to internal constuction etc, the AC resistance does not vary with frequency in a linear manner.
Next, the gain for a common cathode gainstage is Av = -Mu RL/ RL + rp.
Rp is the plate resistance of the tube. We don't need to be concerned with this. RL is R1, the plate resistor. Let's suppose we use a value of 100uf for the value of C1. Fig. 4, the equivalent circuit shows this value of 100uf and its impedance/capacitive reactance at different frequencies.
Notice C1's AC resistance changes with frequency (this is simplified, as reactance is not resistance). This means the real value of RL/R1 is not simply 22k ohms, but is 22k ohms "Plus" the impedance of C1 at a given frequency (complex mathematics involved in order to add them, not simply R1 + C1 impedance). This means that the stage gain varies with frequency. (Not shown, the power supply either uses an inductor or resistor between the rectifiers and C1. Either's AC resistance is so high compared to C1 as to be a non factor.)
As we can see, in order to obtain the most linear frequency response, we should make the value of C1 as large as possible. This will minimize any changes to RL/R1. But this poses a problem in the real world as no capacitor is perfect, as *ESR, *DA, and inductance/self resonance are always present to some extent. Capacitor types, such as electrolytic and tantalums are by far the worst in terms of ESR and DA, which can approach 8%, with inductance and thus self resonance raising its ugly head as low as 2 khzs. (See "Picking Capacitors" by Walter Jung and Richard Marsh.) This can be addressed by using the proper capacitors.
Polypropylene capacitors have a DA of only approximately .02%. But even different polypropylene capacitors have different internal inductance and varying ESR, depending upon dimensions, and whether foil or metalized. Thus physical size, conductor thickness, terminal techniques, can and will make a sonic difference. For instance we were able to listen test several brand polypropylene capacitors.
If you noticed, I have not addressed harmonic distortion (THD) or intermodulation distortion (IMD), which any component can spec. Yet the less expensive components rarely understand, let alone address the problems discussed in this paper.
The power supply should address 100 or 120 hz ripple frequency and ripple currents.
This is an extremely tough challenge.
So what does all this mean? I hope you come to a better understanding how difficult it is to design a proper power supply, let alone the rest of the circuit design. It takes superior quality parts, superior circuit design, even the layout. Even then one common power supply for all stages is nearly impossible to design correctly and work properly. Using CCS (tube or SS) introduces its own problems. Of course the problem of frequency dependent feedback through the power supply is solved if one uses separate power supplies for each stage. However, virtually no manufacturer does.
As mentioned in my opening comments, this article was meant for the general audience, in simple language.
* DF stands for dissapation factor and DA stands for dielectric absorption. Extremely simplified, DF is the reactance of the foils, terminations, and leads. DA is dependent on two molecular level properties: the permanent "dipole moment" and the "polarizability" or the induced change in dipole moment due to the presence of an electric field.
Also see "Picking Capacitors" by Walter Jung, Audio Magazine, Feburary, March 1980, for more details and explanation.