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AudioRoundTable.com: Thermionic Emissions => 4 x 1 Ohm = 16 Ohms (sometimes)

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4 x 1 Ohm = 16 Ohms (sometimes) [message #9105] Mon, 25 July 2005 15:01 Go to next message
Damir  is currently offline Damir
Messages: 1005
Registered: May 2009
Illuminati (2nd Degree)
Reading the specs for some "Partridge" SE OPTs, I found something that can be interesting (if you like OPTs and math and have nothing better to do). The specs say: "Primary impedance Rpr=3500 Ohms, and four secondaries of 1 Ohms - for 4, 8 & 16 Ohms connection." How?

We have turns ratio between the primary, Npr (number of turns of the primary winding), and four identical secondaries Ns1=Ns2=Ns3=Ns4

n = Npr / Ns1-4

We don`t have those numbers, but we know impedance ratio(s):

z = Rpr/Rsec1-4 = 3500/1 = 3500

And from imp. ratio, our turns ratio is: n = z^0.5 = 3500^0.5 = 59,16
Note that z^0.5 is the square root of z.
Simplified, we can "assume" that Npr=5916 turns, and Ns1-4=100 turns.

a)We can connect all four 1-Ohm secondaries in series:
Then we have n1=Npr/(Ns1+Ns2+Ns3+Ns4)= 5916/400 = 14,79
And Rs-a = Rpr/n1^2 = 3500/14,79^2 = 16 Ohms

b)We can connect only three secondaries in series, then we have
n2=Npr/(Ns1+Ns2+Ns3)=5916/300 = 19,72
Rs-b = Rpr/n2^2 = 3500/19,72^2 = 9 Ohms ("close enough" to nominal 8 Ohms)

c)We can connect only two secondaries in series (but probably, better to connect Ns1 & Ns2 in series, then Ns3 & Ns4 in series too, then both series "combinations" in parallel)
n3=Npr/(Ns1+Ns2) = 5916/200 = 29,58
Rs-c = Rpr/n3 = 3500/29,58^2 = 4 Ohms

Simple enough, when we know what is impedance ratio (z), and what is turns ratio (n). Turns ratio is equal to voltage ratio, and if we measure, say, 100Vrms across the primary, and say, 5Vrms on 4-Ohms winding, we have voltage/turns ratio
n=100/5 = 20, and our impedance ratio is z=n^2 = 20^2 = 400. Then our primary impedance is Rpr = z * Rsec = 400 * 4 = 1600 Ohms.

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9106 is a reply to message #9105 ] Mon, 25 July 2005 15:38 Go to previous messageGo to next message
Thermionic  is currently offline Thermionic
Messages: 208
Registered: May 2009
Master
Interesting. Indeed, four 1 ohm secondaries in series do NOT make for 4 ohms, as the impedance ratio is the square of the winding ratio, instead of merely the sum of their individual reflected impedances added. Great post as usual, Damir!

I know that some hi-end transformer makers, such as Plitron and Electra Print, use multiple secondaries tied together to attain a single, fixed value, usually around 5 or 6 ohms reflected Z. The fixed "middle of the road" value is intended to cover both 4 and 8 ohm speaker duties. They claim that better bandwidth is attained by this method.

Thermionic

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9107 is a reply to message #9106 ] Mon, 25 July 2005 17:01 Go to previous messageGo to next message
Manualblock  is currently offline Manualblock
Messages: 4973
Registered: May 2009
Illuminati (13th Degree)
How come the reflected Z doesn't change with frequency? Please excuse if this is a dumb question.

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9110 is a reply to message #9106 ] Mon, 25 July 2005 20:34 Go to previous messageGo to next message
chana  is currently offline chana
Messages: 2
Registered: May 2009
Esquire
all in series =16 Ohms
all parellal = 4 Ohms
two of them parellal then series to the other two =8 Ohms

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9111 is a reply to message #9110 ] Mon, 25 July 2005 23:43 Go to previous messageGo to next message
Damir  is currently offline Damir
Messages: 1005
Registered: May 2009
Illuminati (2nd Degree)
And how four identical 1-Ohm windings connected parallel become 4-Ohms secondary? The same for your 8-Ohms example. Can you post your math? Impedance (z) and turns ratio (n) are different things, z=n^2 - that`s why I posted it, some people are little confused...

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9113 is a reply to message #9107 ] Tue, 26 July 2005 05:54 Go to previous messageGo to next message
Damir  is currently offline Damir
Messages: 1005
Registered: May 2009
Illuminati (2nd Degree)
Not dumb, we know that impedance of the speaker is not a constant resistor, but it changes with frequency. Properties of the OPT (Lp - bass frequencies, Lw & Cw high frequencies, etc.), and tube(s) connected (rp) also impact the frequency response.
But, simplified - we can observe speaker like resistor, and primary load Ra like constant resistance, 3,5kOhms in this example, on some "middle" frequencies of interest.

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9114 is a reply to message #9106 ] Tue, 26 July 2005 06:00 Go to previous messageGo to next message
Damir  is currently offline Damir
Messages: 1005
Registered: May 2009
Illuminati (2nd Degree)
Thanks, and yes, my Plitron/Amplimo toroidal OPTs are 5 Ohms nominal secondary impedance. They have 5 secondaries, connected in parallel. But how they actually wound them (interleaving, etc.) is the "secret" inside the potted unit...:-)

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9117 is a reply to message #9114 ] Tue, 26 July 2005 11:53 Go to previous messageGo to next message
Thermionic  is currently offline Thermionic
Messages: 208
Registered: May 2009
Master
Yep, I've had the pleasure of making the acquaintance of a few Plitrons myself, both PP (5 ohms nominal) and SE (4 and 8 ohms). That's how I knew about the multiple secondaries; the huge bundle of blue wires emerging from the potting epoxy that keeps the contents "top secret." I peel off the little silver "Designed by Vanderveen" stickers from the bottom and stick them on my toolbox for "victory marks," LOL!

IMO, they're just about the best iron mankind has ever made. I have some Tamuras that are certainly quite detailed, coherent, and refined, but the Plitrons do eat their lunch, IMHO.

Thermionic

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9118 is a reply to message #9117 ] Tue, 26 July 2005 14:31 Go to previous messageGo to next message
Damir  is currently offline Damir
Messages: 1005
Registered: May 2009
Illuminati (2nd Degree)
I only wish that those OPTs are little less expensive...:-)
Did you see that M. Vanderveen has www page now, mostly about R&D and cnsultation, but have some pages about new book, etc.
BTW, his book "Modern High-End Valve Amplifiers" is IMO a new "standard" about OPTs and tube amps, I could only wish 100 more pages about amplifiers, classes of operations, etc. I learned much from his books, and from books by M. Jones, too.
Hehe, "Tube Books" is a new message here...:-)

Re: 4 x 1 Ohm = 16 Ohms (sometimes) [message #9124 is a reply to message #9111 ] Wed, 27 July 2005 17:27 Go to previous message
chana  is currently offline chana
Messages: 2
Registered: May 2009
Esquire
Sorry,I made a mistake on 4 ohms tap.It should be two pairs of 1 ohm parallel then connect two of them in series.

Thanks

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