Applications for wide band rf transformers include impedance
matching, voltage or current transformation, DC isolation, balanced / unbalanced
mixing, matching, power splitting, coupling, and signal inversion. Custom wide
band transformers with special combinations of impedance ratio, insertion loss,
frequency response, and current handling are also available."

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WIDE BAND RF TRANSFORMERS

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What are wide band rf transformers?

Wideband rf transformers are simply transfomers designed to provide an
impedance transformation over a broad frequency range. In amateur radio
applications we wind these transformers on ferrite
toroids. A common impedance transformation is 200 ohms to 50 ohms using a
bi-filar winding. Here is an example from our broad
band amplifiers tutorial.

Figure 1. - wideband rf amplifier with shunt feedback and emitter
degeneration

Transformer T1 is a broadband rf transformer.

Designing wide band rf transformers

In the design of these kinds of wide band rf transformers the primary
reactance is usually around 5 times the primary impedance.
With a 200 ohms to 50 ohm transformer, we would allow a reactance of 1,000 ohms
at the lowest frequency of interest. Just as an example consider we were
building a broad band amplifier for the amateur bands and going down as low as
1.8 Mhz.

For this example we would need bi-filar windings which have a reactance
of 1,000 ohms at 1.8 Mhz, this means a required inductance
of around 88 uH. A look through the Amidon data book tells me that ferrite
toroid FT-50-61 as one example can provide me with an AL factor of 68mH / 1000
turns.

This means if 1,000 turns were wound on the toroid it would give us 68 mH.
Yes that IS milli-henries, these are ferrite toroids.

Calculating turns for wide band rf transformers

To wind a wide band rf transformer with an inductance of 88 uH (yes that's
micro-henries) which is in fact 0.088 mh we use the following formula:

Turns = 1,000 X SQRT (L in mH / AL factor)   =   1,000 X
SQRT (0.088 / 68)   =   36 turns.

Our wide band rf transformer needs 36 turns to achieve an inductance of 88
uH.

Winding the wide band rf transformer

Because this is a bi-filar winding for our wide band rf transformer, we need
two lengths of wire which we will "twist" together at a "pitch" of 2.5 turns per
inch or 1 turn per 10 mm. If you anchor one end of the two wires together in a
bench vise and fix the other ends securely in a hand drill (a bent nail or fish
hook helps here) you then gently "stretch" the wires first. Then you slowly turn
the hand drill and notice the two wires "twisting" together, as you proceed you
will notice more and more twists appearing. Stop when you have about 2.5 twists
to the inch. Stretch the wires once more.

Wind 36 turns through the toroid and that is it! To use in an application
such as figure 1 above you need to pay attention to the "phasing". Notice the
two dots on T1 above? They indicate the start of each wire. Use an
ohmmeter to find the start and finish of one winding, mark it in some convenient
manner e.g. coloured pen. The other winding should then be obvious.

Commercially manufactured wide band rf transformers

Coilcraft is one manufacturer of wide band transformers which provide
reliable performance.

The transformers are offered in tapped or untapped configurations and are
packaged in a low-profile DIP-style plastic case. All parts are available in
either a surface mount version or a through-hole version that’s compatible with
standard DIP sockets.

Applications include impedance matching, voltage or current transformation,
DC isolation, balanced / unbalanced mixing, matching, power splitting, coupling,
and signal inversion. Custom wide band transformers with special combinations of
impedance ratio, insertion loss, frequency response, and current handling are
also available.

Designing wide band rf transformers for different impedances

Alright what if you need something other than a 200 ohm to 50 ohms
transformer, how would you go about it?

What I tell you here now is applicable from DC to daylight. What that means
is, it is equally applicable to an audio transformer with a bandwidth of 100 Hz
to 3,000 Hz (for an audio
transformer) as it is to a broadband transformer designed to operate at say
7.00 to 7.50 Mhz. Read on.

Firstly you need to pick either a lower 1 dB or 3 dB bandwidth. Wozzat???
Look at figure 2 below where I present my usual scungy drawing - I'm no good at
this graphic arts caper, not the program, just my lack of artistic talent.

Figure 2. - band pass filter characteristics

Here I've crudely depicted a range of frequencies being passed by a filter
and indicated the 1 dB and 3 db points. A 1 db point is where the power output
is about 80% of the band pass power or 90% of the voltage level. A 3 db point is
where the power output is about 50% of the band pass power or 70.7% of the
voltage level. If you can't understand decibels then you need to look at the decibel page

In your broad band transformer you need to determine the lowest point you can
tolerate in frequency. Entirely for discussion purposes I've selected 5 Mhz for
both 1 dB and 3 dB to demonstrate the formulas. Also I'm going to construct a
broad band tranformer to operate between 14.4 ohms and 50 ohms.

For the 1 db point to be 5 Mhz, I use the formula Lp = R / ( 2 X Pi X Fo) and
for the 3 dB point, I use the formula Lp = R / ( 4 X Pi X Fo). The general
formula for any other dB level is a bit difficult to reproduce here but contact
me and I'll give it to anyone who wants it.

The first formula simply gives you an inductance equal the reactance of R or
in our case we're using 14.4 ohms at 5 Mhz. This results in an inductance of
0.458 uH. The second formula simply produces half that inductance or, 0.229 uH.

Back to the result of 0.458 uH, that could easily be achieved with 10 turns
on a T-50-2 toroid. Alright we have a T50-2 toroid with 10 turns on it, this is
supposed to represent 14.4 ohms at 5 Mhz. To match to 50 ohms all we have to do
is work out the turns ratio. Impedance transforms as "the square of the ratio of
turns". Then 50 / 14.4 = 3.472' and the square root of this is 1.86 so we need
on the secondary 1.86 times more turns or in our case 19 turns.

IF our output were terminated in a genuine 50 ohm load then the square of [19
/10] being the turns ratio would be reflected back giving (if you work it out) a
source of 13.85 ohms.

The CRITICAL aspects here are: a) turns ratio AND; b) final
termination being a genuine 50 ohm load.

What is the upper frequency limit of our wide band rf transformer?

The high frequency limit is influenced by the leakage inductance Lk and
distributed capacitance of the inductor forming a second order low pass filter
and is influenced by a very wide range of factors. The higher the inductance,
then the lower or flatter the low-frequency end but, this comes at a price of
higher Lk and distributed capacitance limiting high frequency response. Often a
compromise is needed for high ratios of frequencies. Although I have never
tested it, I would imagine at least one octave bandwidth could easily be
accomodated e.g. 2.5 Mhz to 5 Mhz or 5 Mhz to 10 Mhz.

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RELATED TOPICS ON WIDE BAND RF TRANSFORMERS

broad
band amplifiers

tuned
circuit amplifiers

impedance

inductance

reactance

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Updated 27th February, 2001

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