Nov
25
INTRODUCTION
Much has been said about triode SE amplifiers with no negative feedback - how good they sound, how lively they present a musical performance and so on. Two easily measurable characteristics that make this type of amplifiers sound different are the amount of distortion produced with its particular spectrum and the high output impedance. This raises the question of whether they sound so good and musical because of these characteristics or in spite of them.
The first time I listened to such an amplifier with no feedback was through a loudspeaker that apparently was not much affected by the high output impedance of these amplifiers. Since I was really impressed with the sound I heard, I decided to do some measurements trying to understand what was going on.
After making these measurements, I became more deeply involved with the subject, thinking about the design of a SE amplifier and the loudspeakers to use with it. Based on this work, my intention here is to examine the output impedance (Zout) and its role in the interface between SE amplifiers and the loudspeaker.
LISTENING TO AN SE AMPLIFIER
After finishing a 300B SE amplifier kit, I connected it to my system and was really impressed with what I heard. I had never heard the violins and the voices sound so natural Although I have other speakers and amplifiers around, the amplifier I was using in my system at that time was a Quad II with some parts upgraded and the speaker was one I had designed and built in the mid 80s, using a Kef bass unit, a Peerless midrange, and a JVC ribbon tweeter as drivers. This loudspeaker has only suffered minor changes and parts upgrade during the years. Although an old design, for me it still sounds good. It is not a high efficiency loudspeaker but with the 300B SE amplifier I have been able to listen at levels I’m used to without any problems.
After some days I decided to look at the whole system trying to find clues explaining the differences between the amplifiers. I measured the Zout of the amplifier and found it to be almost 4 ohms. I knew the loudspeaker very well, and from looking at the notes I made at the time I designed it, I remembered that it presented an almost purely resistive input impedance, with a magnitude between 6.8 and 10.1 ohms from 100Hz to 20Khz (fig. 1). It is a closed box design with about 87 dB/W/m average sensitivity and a highly damped resonance (Q=0.58) at 39 Hz.
In Fig.1,you can also see the loudspeaker frequency, valid from 300 hz up, measured with a low Zout transistor amplifier. With this speaker, driven by a SE amplifier with almost 4.0 ohm of Zout, the big difference I should be hearing because of this characteristic ought to be a stronger and less controlled bass caused by a less damped resonance. From mid bass up the expected differences in frequency response should all fall inside a 1.1dB total range (-0.5 dB / +0.6 dB referred to the nominal 8 ohm impedance).Even taking into account the drop of about 1dB in the high frequency response of the SE amplifier at 20 kHz, the differences I had heard were much greater than what might have been expected from these curves, and surprisingly, the most dramatic differences were in the mid range, with violins and vocals sounding remarkably open, The bass was stronger, as expected, but this was a minor difference compared to the midrange sound. I have to say again that all these thoughts and measurements occurred several days after the initial listening tests, when I noticed the differences in sound.
My reaction to this listening experience seems to be much like most of the described reactions to SE amplifiers. The fact that the loudspeaker I used was fairly insensitive to the high Zout made me conclude that I have to look elsewhere to find the reason for the amplifier’s good sound . This is why I started to look more closely at this characteristic of SE amplifiers in general. If we could lower the Zout without destroying the other aspects of the SE sound, we probably could use these amplifiers with more predictable results with many more loudspeakers.
TYPICAL SE OUTPUT IMPEDANCE
Fig. 2 shows a practical equivalent circuit for single ended output stage, with simplified circuits at mid, low and high frequencies (fig. 2c, d, e). These models are based on the description given by Terman (ref.1). I have simply changed the values to what they are as seen at the transformer’s secondary, instead of at the primary, as in the book. Also, to calculate Zout, RL (the load resistance) is omitted. These equivalent circuits can be improved, especially in the high frequencies, by considering the capacitance in the primary and secondary, but I believe they are suitable as they are for my purpose here After measuring the required parameters for one transformer I used the complete practical equivalent circuit (fig. 2b) with a circuit simulator to calculate the magnitude and phase of the Zout. I followed this with the actual measurements at some frequencies(Fig 3). Although the incremental primary inductance (LP) is not a very constant parameter, the measured results were close to the simulation values. Only at the highest frequencies there was there some appreciable difference - probably the result of not using the distributed capacitances in the equivalent circuit. Measuring other transformers has confirmed that the Fig 3 curves are fairly typical of the simulation of this kind of output transformer using these equivalent circuits.
The decrease in the Zout at low frequencies coincides with a rapid rolloff of the transformer’s low frequency response. One very interesting example appeared in the review of a commercial 300B SE amplifier with a 2.5 ohm Zout at 1Khz, 2.7 ohm at 20Khz and 0.76 ohm at 20Hz (ref. 2).
This low value of Zout at low frequencies may look like a good thing, but it probably happens only because the primary inductance of the output transformer is probably much lower than it should be for extended low frequency response.
This is confirmed by the frequency response plot shown in the review. The amplifier is 9dB down at 20Hz. The low value of the output impedance at 20Hz shows only that the limiting low frequency factor is the output transformer.
RESISTIVE Zout BEHAVIOR
SE Amplifiers with good output transformers should have the Zout with the behavior shown in the fig. 3 or better, with a more extended region of flat impedance. The phase plot shown means that except for the frequencies extremes, you can consider the Zout to be resistive. The region of flat impedance with resistive behavior corresponds to the region where the equivalent circuit of fig. 2c is valid.
I will use this extremely simplified fig. 2c model in all the following analysis. This is an important assumption that must be made to simplify the first visualization of the effects of the high Zout. I will try to show when you should expect this most simplified model to fail, making necessary the use of the other equivalent circuits .
As a first approximation in calculating the output impedance of a tube amplifier with no negative feedback, you can simply divide the plate resistance by n? (n being the ratio between the output transformer’s turns ratio between primary and secondary turns).
Several books state that as a practical rule, output triodes should be loaded with an impedance of about three times their plate resistance for maximum undistorted power output (although some theoretical calculations find a ratio of two to one). Following this rule, the Zout of SE amplifiers with any triode will always be about the same.
At first glance, its value should be one third of the nominal load impedance of the output tap of the transformer, or around 2.7 ohms for an 8 ohm tap. But we should look more carefully using the simplified model of fig. 2c and take in account the transformer’s resistance. As an example, you can do some quick calculations with a typical 300B SE amplifier.
According to the WE manual, the 300B has a 700 ohm plate resistance. Using an output transformer with a 2.5K primary reflected impedance you can calculate the output impedance. You need to measure or estimate its primary and secondary DC winding resistance and use it in the following formulas, which are based on formula (2) on page 206 of the Radiotron Designer’s Handbook.
Zout = (rp+R1) + R2 ( 1 )
n?
where n? = Zp-R1 ( 2 ) R2+RL
Zout = Output impedance
rp = Output tube plate resistance
RL = Nominal load resistance
R1 = DC Resistance of the primary of the output transformer
n = Ratio of primary to secondary turns (it can be measured directly)
R2 = DC Resistance of the secondary of the output transformer
Zp = Reflected primary impedance
If you estimate R1 to be 200 ohms and R2 to be 0.5 ohms, for Zp of 2500 ohms and a RL of 8 ohms. Using formula (2) yelds n?=270. Then, formula (1) gives the value of 3.8W for Zout.
RESULTS WITH MULTIPLE TRANSFORMERS
I measured several parameters of four output transformers for use in SE applications and calculated its Zout when used with 300B tubes. The results are summarized on table 1, along with the measured Zout. These Zout measures were taken at 1Khz. All the results are within 10% of the calculated values. Using a digital multimeter to measure low resistances like 0.6 ohms may introduce a sizable error. Although I have not further investigated the differences between measured and calculated Zout, I believe they can be explained mainly by this factor and by the fact that I didn’t account for the Rp of the particular 300B tube used for the measurements, relying instead on the 700 ohms value given by the manual. All the transformers were measured with the same 300B tube, and changing it during one measurement gave just slightly different results.
TABLE 1
OUTPUT IMPEDANCE VALUES OF FOUR
OUTPUT TRNSFORMERS AT 1kHz
| Transformer: |
A |
B |
C |
D |
| R1(ohms) |
270 |
97 |
128 |
160 |
| R2(ohms) |
0.5 |
0.6 |
0.5 |
0.6 |
| n? |
314 |
265 |
230 |
234 |
| Zp(ohms) |
2970 |
2380 |
2085 |
2175 |
| Zout calc. |
3.69 |
3.60 |
4.10 |
4.27 |
| Zout meas. |
3.73 |
3.96 |
4.46 |
4.37 |
Looking at formula ( 1 ) you can see that the Zout of these amplifiers with triode output tubes can only be lowered (without using feedback) by changing the output transformer parameters. Increasing n? and lowering R1 and R2 will make the Zout decrease. How low can we get? Lets go back to the 300B example. The largest part of the impedance results from the tube’s Rp (around 700ohms for the 300B) made up by the tube Rp (around 700 ohms for the 300B) divided by n?. Formula (2) shows that a greater n? means higher primary reflected inductance.Usually 300B amplifiers use 2K5 to 3K primary reflected impedance. The higher this impedance the lower proportionately the Zout will be. Therefore if you want to lower the Zout you should pick a transformer with a higher primary reflected impedance. In the WE manual 300B tubes are shown operating with loads up till 6K5, although the 6K and 6K5 data is shown only at maximum dissipation ratings. Therefore, it looks as though you can assume that 5K is a reasonable high target.An amplifier using a transformer with this primary reflected impedance should be better from the standpoint of output impedance. But you will need to use higher voltages to keep the output power, and it’s harder to have good frequency response from output transformers of higher primary impedance.
USING HIGHER TURN RATIOS
To see what happens using higher turn ratios, you can calculate the Zout for an hypothetical transformer the same way as before. Use a 5K primary and estimate R1 of 150 ohms and an R2 of 0.4 ohm. For the 8 ohm tap, n? will be 577. You end up with a Zout of 1.87 ohms. Since the characteristics of this hypothetical transformer are those of one that?s optimized for low Zout, I believe that 2 ohms should be about the lowest you could expect from a 300B SE amplifier with no feedback, but still with reasonable output power. Also for any other output triode - and even for tubes used in parallel - you probably cannot get much lower Zout, unless you deviate even more from the old rule about load impedance for maximum undistorted power output (”undistorted” here usually meaning 5% distortion). Everything I have said above applies to the nominal 8 ohm tap. The 4 ohms tap will usually have half of the Zout of the 8 ohm tap. Actually what I have described above for the 5K transformer is like using the 4 ohm tap in an amplifier with a 2K5 output transformer. Therefore when using speakers rated as 8 ohms, if you are willing to sacrifice the output power you can see how it will sound with a lower output impedance using this tap..It should be clear, however, that an amplifier designed to reflect a 5K impedance from 8 ohms should have details in the output transformer, the biasing and the power supply such that it would be optimized for the right impedance, extracting more power and being a better overall solution if done right. And, of course, you could have still a lower output impedance using its 4 ohm tapThe issue as to which output tap to use and of specifying them nominal loudspeaker load is not simple. With tube amplifiers using the tap that better reflects the average loudspeaker impedance will usually result in more output power. To get lower output impedance, the 4 ohm (or lower) tap is always the better option, regardless of the loudspeaker impedance. It’s difficult to balance not only this points, but also the change in frequency-response extension and the different amounts of distortion for different power levels. This is why listening to all tap options is sometimes the only way to decide which one is better for a loudspeaker with a particular amplifier.
EFFECTS OF HIGH OUTPUT IMPEDANCE
As you have seen, the lower limit on the value of the Zout of the SE amplifiers is high makes it important to consider its effects on the system response. Driving a loudspeaker with a high Zout seems to be a bad idea. In general, loudspeakers are designed with the assumption that they will be used with amplifiers that closely resemble a perfect voltage source, which means Zout close to zero. Although the resistance of contacts and cables usually make reducing the Zout of an amplifier below same point like 0.1 ohm a useless effort, in the SE amplifiers, you are dealing with values around 4 ohms. Such a Zout value interacting with typical loudspeakers input impedance will produce a deviation from the loudspeaker intended frequency response.
From the midbass up you can calculate the probable maximum deviation from the original frequency response if we have the amplifier’s Zout value and an input impedance curve of the loudspeaker. You can more or less tell by looking at the imput impedance curve what will happen with the loudspeaker response as a kind of “modulation” of the frequency response curve.
In trying to visualize it you should keep in mind that because of the difference in the effect of the peaks and dips of the input impedance of the loudspeaker and also because of the complex nature of the impedances, the peaks will appear broader and the dips sharper in the frequency response curve than in the original input impedance curve.
TABLE 2
RANGE OF DEVIATION (dB) FOR SPEAKERS RATED 8 ohm
| loudspeaker input range (ohms) |
amplifier output impedance (ohms) |
|||||||
|
5.00 |
4.00 |
3.00 |
2.00 |
1.50 |
1.00 |
0.50 |
0.10 |
|
| 7/10 |
1.16 |
1.00 |
0.82 |
0.60 |
0.47 |
0.33 |
0.18 |
0.04 |
| 6/12 |
2.24 |
1.94 |
1.58 |
1.16 |
0.92 |
0.64 |
0.34 |
0.07 |
| 5/20 |
4.08 |
3.52 |
2.87 |
2.09 |
1.65 |
1.16 |
0.61 |
0.13 |
| 4/32 |
5.78 |
5.00 |
4.08 |
3.00 |
2.37 |
1.67 |
0.89 |
0.19 |
| 3.5/80 |
7.18 |
6.20 |
5.06 |
3.71 |
2.94 |
2.07 |
1.11 |
0.23 |
| 3/500 |
8.43 |
7.29 |
5.97 |
4.40 |
3.50 |
2.48 |
1.33 |
0.28 |
TABLE 3
RANGE OF DEVIATION (dB) FOR SPEAKERS RATED 4 ohm
|
loudspeaker |
amplifier output impedance (ohms)
|
|||||||
|
5.00
|
4.00
|
3.00
|
2.00
|
1.50
|
1.00
|
0.50
|
0.10
|
|
| 3.5/5 |
1.69
|
1.51
|
1.29
|
1.00
|
0.82
|
0.60
|
0.33
|
0.07
|
| 3/6 |
3.25
|
2.92
|
2.50
|
1.94
|
1.58
|
1.16
|
0.64
|
0.14
|
| 2.5/10 |
6.02
|
5.38
|
4.57
|
3.52
|
2.87
|
2.09
|
1.16
|
0.25
|
| 2/16 |
8.52
|
7.60
|
6.47
|
5.00
|
4.08
|
3.00
|
1.67
|
0.37
|
| 1.75/32 |
10.46
|
9.31
|
7.89
|
6.09
|
4.98
|
3.66
|
2.05
|
0.46
|
| 1..5/250 |
12.56
|
11.15
|
9.44
|
7.29
|
5.97
|
4.40
|
2.48
|
0.56
|
THE RESPONSE CHANGE
To calculate the change in the response we should use the following formula:
D(f) = 20log __Zin (f)__ (3)
Zin(f)+Zout
where, D(f) = deviation in dB at frequency f
Zin(f) = input impedance of the loudspeaker at frequency f
For any resistive value of Zout that is not zero, this formula will always give a negative value which corresponds to a loss. But you are looking for the difference between the loss at the maximum Zout and the minimum, which will give the range of deviation from the intended frequency response curve of the loudspeaker.
Ideally we should use the complex values of Zout and Zin but the output transformer model we are using implies a resistive behavior for Zout. Also the peaks and dips in the magnitude of the loudspeaker input impedance usually correspond to points where its phase angle is 0 or very close to it. Because of these facts using just the magnitude of the input impedance and assuming a resistive behavior, will give you the most probable maximum deviation from the intended frequency response of the loudspeaker.
I went through all the 1995 issues of Stereophile and looked at 31tested loudspeakers whose input impedance curves were published. The maximum values for input impedance had to be estimated since the curves are limited to a maximum of 20 ohms. Considering only the frequencies well above the low frequency resonance of the system, the average loudspeaker had an input impedance varying from 4.3 ohms to 15.0 ohms. with the phase going from -28 to +29 degrees. Very seldom a loudspeaker had phase angle of more than 45 degrees or less than -45 degrees (only 2 cases, being the worst a 55 degrees angle). This is fortunate because the error introduced assuming resistive behavior will be small.
MAXIMUM DEVIATION RANGE
Based on the above assumptions, tables 2 and 3 give the estimated range of maximum deviation from the intended frequency response of the loudspeaker for different values of input impedance and of amplifier’s Zout. Table 2 is for loudspeakers which would be rated as 8 ohms and table 3 as a table for loudspeakers rated as 4 ohms. I chose the range of input impedance so that, as much as possible, this nominal impedance would split the range in half. Hence, in table 2 a 5.00 dB range corresponds to ± 2.50 dB referred to the level corresponding to the 8 ohms nominal impedance.
For these tables the error introduced by considering Zin and Zout resistive is always less and most of the time much less than 0.7 dB for any of the values in the tables for a difference in phase angle below 45 degrees. But loudspeakers can have all kinds of input impedance curves and, although it doesn’t happen frequently , if the phase difference gets higher you could have larger errors. The intent of these tables is to show how the Zout affects the system response, allowing us to look at the broad pattern. I did not intend to exhaust all the possibilities.
HIGH FREQUENCY EFFECTS
Now look at what will happen at the very high frequencies. Should the equivalent circuit of fig.2e be used here? With dynamic loudspeakers the voice coil inductance of the tweeters will usually have an effect on the phase of the loudspeaker input impedance that corresponds to an inductive behavior. This is similar to the effect of the transformer’s leakage inductance on the phase of the amplifier Zout. This keeps the difference in phase angle small and this reduces the need to use the model of fig.2e for evaluating the effects of the high Zout at high frequencies with dynamic loudspeakers. As long as the change in the magnitude of the Zout at high frequencies is reasonable we should have no surprises here and can still consider the Zout resistive when using formula (3). This also holds even when impedance compensating networks (Zobels) are used. Only with output transformers with very limited high frequency response driving loudspeakers with capacitive behavior (like piezo tweeters) we should need to take a closer look at these frequencies, because of the probably high phase difference.
All the considerations above are valid through the frequency region that’s far from the resonant frequency of the system’s woofer. Near the system’s resonant frequency you can still try to use the same approach as a rough guess but it may give wrong results. You cannot simply use the idea of “modulation” of the frequency response curve by the loudspeaker input impedance curve without further care.
Not only does the falling frequency response make it difficult to visualize the effect of the output impedance, but in vented systems the change in the alignment produced by the high Zout will also change both the value and the frequency of the impedance peaks. There are also other factors - including the primary inductance of the output transformer - that may affect the frequency response of the system, making the use of the equivalent circuit of fig. 2d necessary to understand what happens. But this deserves an article of its own.
REFERENCES
ref. 1 - Terman - Electronic and Radio Engineering (1955) - pg. 341
ref. 2 - Stereophile - March/1995 - pg. 120
ref. 3 - Reich - Theory and Application of Electron Tubes (1944) - pg. 228 - 232
ref. 4 - Dammers, Haantjes & Van Suchtelen - Application of the Electronic Valve in Radio Receivers and Amplifiers. Vol II (1951) - pg. 97-101
ref. 5 - Langham - High Fidelity Techniques (1950) - pg. 38 - 41
(published in Glass Audio 3/97)
? Copyright 1997 Audio Amateur Corp.
Comments
Leave a Reply
You must be logged in to post a comment.