B.1) Introduction

An RF Bridge is used in the experiments to measure the signal travelling in one direction within a coaxial cable. There are several different types of Bridges and Directional Couplers that can be used to make directional measurements but the RF Bridge intended to be used for these experiments is made specifically for this purpose and is of a Tandem Transformer type. The RF Bridge uses a termination to balance to 50 Ohms and and does not work properly if used at another impedance and this characteristic is used as partial proof of the measured transmission lines being 50 Ohms.

B.2) Circuit Description - Transformers

The Bridge circuit used is shown in the figure below.

There is a very complete mathematical analysis of this circuit at http://www.members.tripod.com/michaelgellis/direct.html but it is hard going and a simpler way to understand the circuit may be follows.

The circuit comprises of a current transformer at the top of the drawing (Tc) and a voltage transformer (Tv) at the bottom.

The Voltage Transformer (Tv) and the Current Transformer (Tc) are identical transformers so both have the same basic turns ratio but Tv is used as a voltage step down and Tc is used as a current step down. To make the calculation easy, lets assume a turns ratio of 10:1 for Tv and 1:10 for Tc.

If we assume that there is +1 Volt at the Input to the bridge and negligible voltage drop across Tc primary, there will also be approximately +1 Volt at the bridge Output. If the Output of the bridge is externally loaded with 50 Ohms, then the current through Tc primary will be

I = V/R = 1/50 = 20 mA

We can then calculate the secondary conditions ready for the description:-

Transformer Tc

Primary current = 20 mA

Transformer ratio = 1:10

Secondary Current = 20/10 = 2 mA

Transformer Tv

Primary voltage = 1 V

Transformer ratio = 10:1

Secondary Voltage = 1/10 = 0.1 V

B.2) Circuit Description - Reflected Direction, Causing Cancelling

When the current (shown by arrows) in the current transformer Tc primary passes from right to left, the current in the Tc secondary also passes from right to left.

The current transformer Tc secondary is presented with a high resistance from the voltage transformer Tv secondary at point A and so passes all of its current of 2 mA through the 50 Ohm termination. The current of 2 mA passing through the 50 Ohm termination results in a voltage of + 0.1 Volts at the point A.

The current in the primary of the voltage transformer Tv will always pass downwards no matter what direction the current flows in the current transformer Tc. This causes the secondary voltage of Tv to be +0.1 Volts at point A in relation to the Coupled Output. As the point A is already held at +0.1 Volts by the current transformer secondary (Tc) there will be 0 Volts at the coupled output and therefore no output current.

B.2) Circuit Description - Forward Direction, Causing Addition

When the current in the current transformer Tc passes from left to right, the current in the secondary also passes from left to right.

The current transformer Tc secondary now passes its current in the same direction as the voltage transformer Tv secondary current and so all of the 2 mA from Tc passes through Tv secondary and the coupled output resistance of 50 Ohms. No voltage is generated at point A which remains at 0 Volts due to the fact that Tc is a current transformer and able to source 2 mA without generating a significant voltage.

The current in the voltage transformer Tv again passes downwards causing a secondary voltage of 0.1 Volts but the voltage at point A is now being held at 0 Volts, so the 0.1 Volts generated across Tv secondary causes the coupled output to become -0.1 Volts. The negative voltage of course resulting in the coupled output voltage being 180° out of phase with the bridge input voltage.

Thus the bridge is directional and balanced by Tc, Tv, Coupled Output load and the 50 Ohm Termination. It can be seen that it is the 50 Ohm Termination which gives the bridge the characteristic impedance of 50 Ohms and using for instance a 75 Ohm Termination would make it a 75 Ohm Bridge.