Parafeed Fun
First Web Edition 1 Jan 07, Last update 31 Jan 07

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Related pages:
Normal Transformer / LC Tank Damping
Load Lines with Load Line Spread Sheet

There have been a few Parafeed spreadsheets popping up on the Internet and with some prodding from Mikey, I decide to make one of my own over Christmas.  A nice man from NY helped by introducing me to the complex functions in Excel. The last time I did calculations like this, I did the calculations the hard way and did the complex math long hand. The complex functions in Excel make life much easier. Long hand math is for homework assignments in college.

The first step was to use Pspice to get a few "Error Free"  plots to check the spread sheet against. This will also let me know what plots I want to put in the spread sheet
The plots start at 1 Hz. This is useful for seeing trends below 20 Hz, but what we normally care about is what is happening at 20 Hz and higher.

The plots stop at 1000 Hz. The model we are using isn't valid above 1000 Hz because it does not include parasitic capacitances and leakage inductance.
The trick will be to keep our eye on the "big picture." We want to:
  1. Optimize the power supply rejection, more specifically, power supply rejection divided by the output voltage
  2. Optimize the output impedance of the amp, i.e. don't throw away the damping factor.
  3. Optimize the load line on the tube and
  4. Optimize the frequency response of the output over the entire audio range
  5. WITHOUT messing anything else up and WITH having enough cash left over at then end of the day to enjoy a glass of original Dr Pepper from Dublin Dr. Pepper.
Part 1
We'll look at a simple model and vary the plate choke, Parafeed capacitor and transformer primary inductance one at a time to see what they do.

Part 2
We'll look at adding a few losses to the circuit.

Part 3
We'll add DrP (Damped Resonance Parafeed.)

Part 4
I'll introduce an Excel spread sheet to run these plots.

Part 1:
The Simple Model

Here is a simplified model of a Parafeed circuit. The DCRs of the plate choke and transformer are omitted and the impedance of the B+ is set to zero.  Because the losses in the iron and copper are not included in the model, when we see resonances, they will be are larger than in real life.

Here is a basic frequency sweep with a huge 40,000 Henry plate choke. This is equivalent to a CCS feeding the tube instead of a plate choke.

Now lets drop the plate choke down to an affordable 40H. My normal rule of thumb for a plate choke is it should be 8H for every kohm of load or larger. So with a 5K load, the plate choke should be about 40H or more.  Other people use 10H per kohm of load as a rule of thumb. The difference between 40 and 50H isn't that big. We normally don't care about the phase shift at 20 Hz to the speaker (red trace in middle plot), but it is included in this plot anyway.

The running of plots one at a time makes it difficult to see what is changing. So what I'll do next is sweep one parameter at a time (plate choke, Parafeed cap and primary inductance) so we can see what each parameter does.

Part 1.1
Let's see what the Parafeed cap does at 0.2 uF, 2 uF, 20 uF and 200 uF.

Lets run plots with the Parafeed cap set to 0.2 uF, 2 uF, 20 uF  and 200 uF. For clarity, I deleted the phase at the load (the speaker). We care more about the phase angle of the plate load seen by the tube than the low frequency phase at the speaker. We can see more capacitance leads to a lower - 3 dB frequency (good), a flatter phase angle on the load line (good) but a lower impedance load line (not so good if it occurs in the audio range.)
C para sweep, vout

--- There are two other things we care about in an audio amp. ---

There are at least two other things we care about in an audio amp. The top two things that come to mind are the power supply ripple rejection and output impedance (damping factor).

For both curves: Lower is better, flat is better.
First  lets look at the results displayed as Power Supply Rejection and Output impedance.

Now lets decide how we want to display rejection of B+ ripple, PSRR. Lets examine the plot below to see what we learn.
PSSR normalized to Voutput

In general,

Hint: The less you work a capacitor (change the voltage across it), the better it will perform.

Overall, I'd start a design with a moderate Parafeed cap: 8 uF / 1K of plate resistance (1K = 8 uF, 2k = 4 uF). More capacitance will give better damping. A lower value will roll off the -3 dB point so as to not drive the Parafeed transformer as hard if saturation is a problem. If I wanted to raise the -3 dB point (say from 20 Hz to 40 Hz), my preference would be to use the large Parafeed capacitor for good damping and roll the -3 dB point off in the drive to the output stage .

Part 1.2
Let's see what the plate choke does at 4H, 40H and 400H.

Let's  examine what happens with the plate choke at 4H, 40H and 400H with the Parafeed cap (Cpara) set to 2 uF and then to 20 uF. 


Here's the power supply rejection (top) output impedance (bottom) with the plate choke at 4H, 40H and 400H.
For both curves: Lower is better, flat is better


Here's one where the PSRR isn't normalized. When it is normalized, it is easy to see that at 4H, the power supply noise is higher than the music below about  80 Hz. When it isn't normalized to the output response, we completely miss this wonderful discovery.

In general,

The improvement in damping from smaller plate chokes can be easily lost to the higher -3 dB points and to lower output power due to elliptical low impedance load lines and the loss in "real" B+ noise rejection. The other issue with using a small plate choke to improve the damping is the damping runs through B+ and not directly to ground. For the plate choke, I recommend a moderate (8 H/K of primary reflected load impedance) to high values (400H or CCS drive.)

Part 1.3
Let's examine what happens with the primary inductance of the transformer at 4H, 40H and 400H

Let's examine what happens with the primary inductance of the transformer at 4H, 40H and 400H with the Parafeed cap (Cpara) set to 2 uF and then to 20 uF. 


Now for the PSRR and output impedance.


I've been told that most good Parafeed Transformers will run 50H of primary inductance per kohm of rated primary impedance. This means a 5K primary should run around 250H.

Part 1.4
Summary of  what we learned with the simple model

Part 2
Let's add a few losses to the simple model

Lets add the DCR (DC resistance) of the choke and the DCR of the transformer to the model. These parasitics are easy to measure, calculate and understand. The core loss isn't easy to measure and most manufacturer's won't give it to you.
  • DCR of the choke is fairly straight forward. It adds a voltage drop from the DC bias of the tube.
  • The DCR of the transformer adds insertion loss to the transformer.
    • This means if we put one watt in the input, we get less than one watt on the output.
    • There are several ways transformer manufactures deal with the losses from the DCR.
      • The turns are set to the ideal turns ratio. Both the reflected primary impedance and the output voltage will be off.
      • The turns are compensated so the loaded output voltage is correct (this is usually done on power transformers.)
      • The turns are compensated so the loaded primary impedance is correct (some audio transformers.)
      • A combination of the above.
    • I'm using an impedance compensated model for the transformer (the primary impedance is correct.)

Sweeping the plate choke at 4H, 40H and 400H, we get an output response that looks like the following. It is kind of hard to tell the difference between the two except that the output is about a dB lower.

Subtracting the two outputs gives us a magnified view of what is changing.
The top plot shows that the DCR of the plate choke adds a bit more power supply rejection when the plate choke is small (4H).
The bottom plot shows the DCR of the transformer adds 1 dB of loss at 1 kHz. The DCR of the choke adds some voltage gain at subsonic frequencies.

The effects of the DCR on the output impedance can be see in the following plot. At 1 kHz, the DCR of the transformer makes the damping factor 1.26 times worse.

The output impedance of the amplifier is dominated by the plate resistance of the tube followed by the resistance of the transformer windings. If you want better damping in a SET or Parafeed amp with a given tube, you have to give up some output power and use a higher primary impedance on the transformer. A 10K primary should have two times better damping than a 5K and a 5K should be twice as good as a 2.5K. Remember TANSTAFL? To get the better damping we give up something. If 2.5K is the resistance needed for maximum power out, the 5K and 10K will give progressively lower output power for the same tube and bias point.

Part 3
DrP, Damped Resonance Parafeed
It's more than an excellent soft drink.
(Plots and long diatribe to be added later)

With good iron in a Parafeed power amp, DrP doesn't help too much. You can some times use it to tweak a bit more low frequency power out.

If we use budget iron, Damped Resonance Parafeed adds some additional parameters we can tweak to trade off power handling vs damping vs -3dB points.

In a driver stage or preamp, DrP can greatly reduce the low frequency resonance of the unloaded Parafeed tank without having to add a resistor across the grid choke or Parafeed transformer to ground. This is good because it gets us a little more voltage gain out of the circuit and greatly reduced the loading on the tube (which makes the tube sound better in my book.)

Because of the DrP resistor in series with the DrP capacitor, the Parafeed capacitor shorts out the "sound" of the DrP cap at almost all frequencies. This means the DrP cap can be a slightly lower grade than the Parafeed capacitor. I happen to like metal foil capacitors. DrP means I could use a metal foil (film and foil) capacitor for the Parafeed capacitor and then use a metalized cap for the DrP cap.

Click on this link for technical discussions on Transformer / LC Tank Damping

Part 4
A Spread Sheet to Play With

To use this spread sheet, you'll need to have your EXCEL install disk in hand and do the following:

    In Excel, Click on

             Analysis ToolPak      [not the Analysis ToolPak - VBA]
                Put your Excel install disk in the CD drive and follow the rest of the instructions.

Click here to get the Excel File: Parafeed Circuit Spread Sheet

The Excel spread sheet models this circuit from about 1 Hz to 1 kHz.
Circuit Modeled in Spread Sheet

The data section of spread sheet looks something like this:

Spread Sheet Inputs
The spread sheet will model two designs at once so you can compare them.
The normal things we care about are listed in a table format
Spot Frequency Check
Cell K3 (30 Hz) lets you input a frequency for a detailed analysis. You can enter any frequency you want between 1 Hz and above 1 kHz.

One thing that is missing is an analysis of the transformer saturation limited allowed output power vs frequency. I'm not sure this is a big deal to not have it.

  1. I'm not sure if we can get consistent data from the transformer manufacturer's that is taken at the same level of peak distortion, input loading, output loading etc.
  2. I'm not sure if anyone other the Paul Joppa could use that curve without messing up all the other parameters.
The "normalized" load impedance seen by the tube vs frequency plot looks like the following.
Load impedance seen by tube

The small signal frequency response and power supply rejection is given in a plot that looks like the following. For dB out, flat and a low - 3dB is best. For PSRR, in this plot more negative is better (-50 is better than -40). If you look close, you'll see the 1 kHz Vout is not 0 dB. This is because the plot shows the effects of loading on the tube.
small signal

Part 4.1
Lets Examine a Driver Stage.
We see that the output peaking (Design 1) is 13.4 dB and if we increase the capacitance by adding the DrP cap with no series resistance, the peaking is 11.2 dB. This is a hint that just adding more capacitance won't kill the peaking easily.

Lets add the estimated value for R DrP and see that the peaking drops from 11.2 dB down to 5.32 dB.

Just for kicks, we'll use the Excel Goal seek function to try to drive the peaking down.

Goal Seek function is found under
    Goal SEEK

The trick to using goal seek is not to get greedy all at once. Don't go for zero on peaking. Go for a little smaller than the existing peaking. If it doesn't work, try a different goal and it may work. In this case, the goal seek couldn't find a better value than the estimated value.

With a 0.33 uF DrP, the output response's improvement can be seen in the following plot.

DrP works better with the DrP cap set to 2 to 3 times the Parafeed capacitor. Using the suggested DrP resistor, 2X cap has 3.19 dB peaking where 1X had 5.32 dB peaking. After running the goal seek optimization, the 2X gets 0.01 dB better. Not that big of a deal. This also shows that the DrP resistor isn't very sensitive to its value. We changed it 10% and got almost no change.

Lets check a 1 uF DrP. Going from 2X to 3X buys us 1 dB less peaking. For 1 dB I'd just use the 2X value.

The historical way to kill the subsonic peaking in a driver is to put a resistor across the grid choke. This kills the peaking, but it makes the driver tube work harder. Lets use Goal seek to pick a damping resistor across the grid choke and compare it to a 2X DrP damping cap. Remember to use small steps when tweaking in the peaking by changing part values with goal seek.

To get "0 dB" peaking we need to put a 36K resistor across the grid choke. 

At 1 kHz, the grid resistor costs us 1.5 dB in gain over adding the DrP cap.

Now for the interesting plot.
I'd much rather have the 166K load on the tube than the 34K load on the driver tube.

Now to be fair to the Resistor across the grid choke damping method. Lets increase the resistor across the grid choke until the load at 40 Hz is 166K. This requires using a 1.09 megohm resistor across the grid choke. The peaking is now 13.6 dB with the resistor across the grid choke instead of 3.2 dB with the 2X DrP configuration.

Like I said, DrP. . .
it's more than an excellent soft drink.
Here's the before and after schematic. Note: R4 and R8 aren't real resistors in the circuit.

Here's the DrP plots. The output peaking is slightly different than the Excel spread sheet mostly because the Pspice plot uses fine frequency steps and the Excel plot uses course frequency steps.

Part 4.1.1
Is This Gain Peaking a Problem?.
Lets not lose track of the ball: Thoughts on 1-20 Hz gain peaking issues:
Play safe and have fun out there.
If you have questions or comments, contact me through Asylum Mail.

First version 01 Jan 07, Last update 31 Jan 07