Coax Continuity Tester: The object of this project was to play around with logic circuits (TTL) and computer software for logic circuit design and analysis. It is trivial to test the continuity of an ordinary length of coax using an ohmmeter. Touching the probes to the center conductor at both ends should show near zero resistance, and the same for the shield. Probing between the center conductor and shield should indicate an open circuit (infinite resistance).

The tester pictured above has three light emitting diodes (some additional wiring is not visible under the PCB). When a cable is connected between the two SO-239 jacks (or the RCA phono jacks), pressing the left pushbutton (left end of circuit board) tests the center conductor. Pressing the other button tests the shield. The green LED indicates that the tested conductor is good. The red ‘Open’ LED indicates a break in continuity, while the other red ‘Short’ LED indicates a short circuit. Since the unit is battery powered I thought it would be prudent to include a power indicator as well (lower left LED illuminated).

I first drew the circuit using the program Logisim. After making a couple of simplifying revisions I constructed the project on a breadboard and it appeared to work as intended. At this point I became curious as to whether I could write out a logical expression for the ‘Good’ indicator, based on the four inputs (center left, center right, shield left, and shield right). Using pencil and paper to construct an equation I made mistakes, inevitably ending up with mismatched parentheses or a missing or superfluous ‘not’ symbol. So instead I wrote a simple computer procedure that accepts a list of equations as input (each equation corresponding to a single logic gate) and additionally a target expression (something to solve for). By iteratively substituting symbols the procedure converts the target to a form that references only input variables (i.e., stopping when no further simplification is possible).

Using this ‘helper’ utility I was able to obtain the desired expression for the ‘Good’ indicator. Next, a Google search for ‘logic simplifier software’ yielded several relevant resources. The one that I ended up using is called Logic Friday (another wonderful free program). My goal was to create three expressions, one for each indicator LED, then to simplify each of them, and in the end produce a simplified combined circuit. However, when I entered the ‘Good’ expression into Logic Friday the program’s truth table included two unexpected rows. After wasting a lot of time proofreading the circuit and double-checking its breadboard implementation a question popped to mind: Had I really tested the exact combination of inputs that unexpectedly evaluate as good? The truth table was saying that if one of the coax conductors was open and the other not, AND if both buttons were pressed simultaneously the ‘Good’ indicator would illuminate. Upon testing these exact conditions that was what happened. This observation led to a minor change in the logic, after which the truth table exhibited by Logic Friday consisted of only two rows, corresponding to a good center conductor and good shield.

I am omitting details from this account but supplementary information may be found here. The logic diagram shown below is the circuit that was implemented (photo at the top of this description). It is revision 4 of the original seat-of-the-pants design. (Note that the two fault LEDs are themselves inverted).

Logic Friday includes a ‘Minimize’ option that accepts a messy equation as input, and produces a minimized version of the same logic. It is then possible to translate the minimized expression back into a circuit. Combining separate minimized circuits without further simplification leads to the following diagram.

Since the diagram above represents a combination of three independently derived circuits, it includes some redundant elements (duplicate inverters). In general, minimizing logic in a small-scale circuit such as this one is not necessarily the same as minimizing the circuit, due in part to the way that gates are packaged in ICs. Other considerations include the ready availablity of ICs or their cost, if they must be purchased.

Coax continuity tester: TTL/coax_tester_demo.mp4

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