Transformers

It became apparent after knowing what everything did, that the transformers in an amp had a huge influence on it's "sound." I always wondered why some amps weighed a ton, while others didn't. Most of it has to do with the amount of iron in the transformer. I also always wondered why some amps has round transformers in them, and some had square ones. Now I know. Actually I think I now probably know a lot more about transformers than I really care to, and somehow all this extra information has diminished my social skills. It's hard to talk to people when you say stuff like:

"8H per kohm of reflected load seems to be a general rule of thumb for audio amps, and working backwards, this would give me 53H of Lp. I'm wondering if this is way over the old Fender guitar OT measurements? What do you think?"

Here is an excellent primer on transformers from obsoleteelectronics.com.

From the same site, here's a good run down of load impedence.

What's a Toroidal OT, and how does it differ from an E1?

Interesting post by Mike LaFevre regarding transformer core materials and laminations. (From Duncan's Amp Pages.)

Useful info from Harp Amps regarding transformers and impedence for Fender tube amps.

Output Transformers Explained (A fantastic primer from Aiken Amps)

General

There are several things that are important in getting an output transformer made. The main parameters are: (a) the reflected primary impedance for a given secondary load impedance, which must match the needs of the particular tube being used, (b) the primary inductance, which determines the low frequency response, (c) the primary leakage inductance and capacitance, which determines the high frequency response, (d) the power handling capability, which determines the necessary core size and wire size, and (e) the mechanical details, such as the mounting style (upright "X" mount, laydown "Z" mount, etc.), the lead color and length, the use of end bells, the finish, shielding, etc.

Reflected impedance

An output transformer has no impedance by itself (ignoring primary inductance/resistance for the moment, which is a different subject). It simply reflects the impedance load on the secondary back to the primary.
A transformer has a turns ratio which can be measured by putting an small AC voltage across the primary and measuring the resulting secondary voltage. The resulting voltage ratio is the turns ratio (you can also put a small voltage across the secondary and measure the resulting primary voltage, which is usually easier, because the voltage is higher and there is not much secondary resistance to introduce measurement errors - but watch out for high voltages on the primary if the turns ratio is large!).

The impedance ratio is the square of the turns ratio, which is also the square of the voltage ratio, as shown in the following equation:

Zp/Zs = (Np/Ns)2 = (Vp/Vs)2

If you put 1VAC across the secondary, and measure 20VAC across the primary, you have a turns ratio of 20:1, which corresponds to an impedance ratio of 400:1. This means that if you put an 8 ohm load across the secondary, you will get a reflected impedance of 3.2K ohms across the primary. If you put a 4 ohm load across the secondary, you will get a reflected load of 1.6K ohms.

For example, if you have a transformer designed for 4.3K : 8 ohms, you can apply a 1 volt AC signal across the secondary 8 ohm winding, and you should see 23.18VAC across the primary, which corresponds to a 23.18:1 voltage ratio or a 537.5:1 impedance ratio, which would reflect an 8 ohm load back as 4.3K.

As you can see, the transformer has no inherent impedance, it merely reflects the load impedance back to the primary.

Primary inductance

The transformer does, however, have a primary inductance, which has a direct effect on the low frequency response of the transformer. The -3dB low frequency cutoff point can be determined by the following formula:
f = Z/(2*Pi*L)

where Z is the primary source impedance (generally speaking, this is the reflected impedance in parallel with the source impedance presented by the tube's plate) and L is the primary inductance.

This means that if you want better low frequency response from your transformer, you have to increase the primary inductance, which means a larger core and/or more turns on the primary.

Primary leakage inductance and capacitance

Unfortunately, when you increase the number of turns, you also increase the capacitance and leakage inductance, which then limits the high frequency performance. The leakage inductance is proportional to the square of the number of turns, so you must decrease the number of turns to reduce the leakage inductance, but this is at odds with the need to increase the number of turns for good low frequency response. In addition, the flux density may be exceeded if you reduce the number of turns. Different winding techniques, such as interleaving, can help reduce the amount of leakage inductance, and improve the high frequency response.

The formula for calculating the high frequency response is:

f = Z/(2*Pi*Ll)

where Z is the primary source impedance and Ll is the leakage inductance.

In addition to high frequency response rolloff, the transient response of a transformer is affected by the leakage inductance. Large leakage inductances can cause "ringing" at sharp transitions, such as a square wave generated by an amplifier driven into clipping.

The capacitance is also increased as the number of turns is increased, and acts to limit the high frequency response as well.

Power handling capability

The two things that determine the power handling capability of the transformer are the core size and the gauge of wire used to wind the transformer. The core size is proportional to the power and the required low frequency -3dB point. A transformer rated for 50W at 80Hz is much smaller than one rated for 50W at 20Hz. The other factor in determining required core size is the number of turns that will fit on the bobbin. If you increase the power rating, you must increase the wire size, which means that less turns will fit on the same size bobbin, so you must increase the bobbin and core size to accommodate the extra turns.

Mechanical

The mechanical factors vary depending upon the application. Typically, it is a good idea to use end bells on both sides for shielding, although some manufacturers (Matchless, for example) will mount the transformer in a "laydown" or "Z" mount, with only an end bell on top. This can sometimes lead to hum or interference inside the chassis. However, this is a very stable mechanical design, because the mounting hole pattern is as wide as possible, and the center of gravity of the transformer is much lower, which means that is can withstand shocks better without being ripped from its mounting holes, but if the amp is subjected to that kind of mistreatment, something else will probably fail as well. I prefer the traditional stand up or "X" mount, with an end bell on each side, with the longest horizontal axis of the core parallel to the chassis to keep the transformer CG as low as possible. Wire length and color are chosen for the particular application.

Conclusions

As you can see from the above explanation, the number of turns is determined primarily by the required primary inductance for the desired low frequency response point, but the high frequency response and transient response will suffer if the number of turns is made too large. In general, there is a minimum necessary primary inductance for a guitar amplifier to achieve the necessary frequency response to reproduce the lowest note on the guitar. It is best to design the transformer for a low frequency cutoff point somewhat lower than this, so the response is not -3dB down at this frequency. Generally it is best to design for half this frequency to shift both the low frequency point downward to make the response balanced throughout the guitar range, and to push the phase shifts down further out of the passband. The overall amplifier low frequency response is then independent of the transformer, and can be set by the circuit components. If the number of turns is increased above this, there is no real gain in low frequency response for a guitar, but the high frequency response and transient response will suffer greatly. Therefore, an "overwound" transformer, if wound with more turns than needed, will actually harm the response rather than help it.


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