Friday, February 12, 2021

Math of Transformers

Purpose: To understand briefly the math of the forces at work in a transformer, especially an impedance transformer for RF antenna systems.

Scope: AC circuits only, including 50 Hz power, 5 GHz microwave, and everything in between.

Math:

Ohm's law:

    V = I R

    I = V / R

Generalized to complex domain (for alternating currents with reactance) becomes:

    V̇ = Z İ ₍₁₎

    İ =  V̇ / Z ₍₁₎

Faraday's law: A changing magnetic field (ΔΦ/Δt) induces a voltage (Emf = V), and a changing voltage induces a magnetic field based on the number of turns on the ferrite core (N):

    V = -N ΔΦ / Δt (2)

Electrical power:

    P = I V

Combined with Ohm's law:

    P = V² / Z

The magnetic field induced on the ferrite core by the input in turn induces a voltage on the output (see caveats):

    ΔΦ1 /Δt = ΔΦ2 / Δt

Insert Faraday's law:

    -V1 / N1 = -V2 / N2

    V2 =  (N2 / N1) * V1   <-- This is the critical equation for a voltage transformer

Because energy is conserved and transformers are (by design) efficient (with efficiency η):

    η P1 = P2

Insert Ohms law:

    η V1² / Z1 = V2² / Z2

And if you substitute the voltage transformer equation:

    η V1² / Z1 = ((N2 / N1) * V1)² / Z2

    η V1² / Z1 = (N2 / N1)² * V1² / Z2

    η / Z1 = (N2 / N1)² / Z2

    Z2 = (N2 / N1)² * Z1 / η   <-- This is the critical equation for an impedance transformer

Both voltage and impedance transformations occur, but usually only one equation is important for the specific application.

Caveats: Saturation and efficiency of the toroid core are dependent on its size and chemistry and the frequency and amplitude (power) of the driving signal. Saturation is when f1 no longer equals f2.

Example 1: A perfectly efficient (η=1) transformer with 3 primary windings (N1) and 21 secondary windings (N2) has an output voltage that is 7 times the input voltage and an output impedance 49 times the input impedance. If the desired output impedance is 50Ω, the target input impedance is 2450Ω.

Example 2: If the transformer is 95% efficient (η=0.95) with the same setup as Example 1 and an input impedance of 2450Ω, the resulting output impedance will be 52.6Ω.

Tuesday, December 29, 2020

Packet Radio

Minimum physical setup for connecting to the SF ACS setup is a 2m radio, TNC (physical/hardware or software), and terminal or packet software. "Standard" ACS setup is FT-2400, Kantronics KPC-3Plus TNC, and a Windows computer running Outpost. Tons of alternatives in each category are possible. One example is KE6JJJ's setup: https://www.reddit.com/r/amateurradio/comments/64skvj/packet_bbs_in_san_francisco/

Some prefer software TNCs (free, cross-platform, and fully functioning so long as the computer doesn't go to sleep) like Direwolf, AGWPE, or UZ7HO. Many folks like using a software TNC combined with a SignalLink (USB bidirectional audio card) to avoid tying up the primary system speakers/mic with packet. For a hardware TNC, I personally have an AEA PK-88, which has fewer functions than the KPC-3P, but does fine enough for me (especially for the price I got it). Some radios (e.g. Kenwood TM-D710G) have built-in hardware TNCs, which eliminates one of the biggest hurdles: connecting the TNC to the transceiver.

Instead of Outpost, I prefer running a serial terminal with automatic logging (Putty on Windows or Minicom in Linux).

A monoband radio isn't necessarily ideal. It depends on whether or not you want to devote a radio to packet. I personally prefer to have only dualband radios (or better) to conserve desk space, ideally true dual-channel radios (e.g. Kenwood TM-V71A), allowing voice and data at the same time. I don't necessarily leave packet running all day, unless it's part of an activation.

The cable between the computer and TNC is typically just a USB to DB9 straight-through (not null) serial cable, possibly with a DB9 to DB25 adapter, depending on your TNC.

As mentioned above, the hardest (or most annoying) part of it all is to make (or buy) the cable between the TNC (or computer, if using a software TNC) and the transceiver. The cables may be able to be found by searching online, or fabricated by combining the right connectors (e.g. from Digikey) and soldering them according to the TNC's and radio's operating manuals. (Debugging can be a pain, and depending on your soldering skills, may require periodic repair when solder joints break.)

To debug, check each of the 4 lines (Gnd, Rx, PTT, Tx) with an ohmmeter, then test each of the operation of each of the 3 functions (Rx, PTT, Tx) individually. (The AEA PK-88 manual has decent instructions how to do this, which are applicable to nearly any TNC.) To test Rx, turn the radio's squelch off, and the TNC's decode (DCD) light should illuminate. You may need to adjust a gain setting on the radio. To test PTT, put the TNC in CONVERSE mode and send a test string (e.g. "TEST TEST TEST TEST DE KJ6LDJ"). Be sure to push Enter at the end of the string to trigger the TNC to start sending. You should see the TNC's SEND light illuminate and the radio key up. To test Tx, do the same as the PTT test, but have a second radio on the same frequency. You should hear the beeps and boops. As with Rx, you may need to adjust a gain setting in the transceiver.

Once the hardware is all set up, the software is generally not as complicated for simple connection to the BBS. With a hardware TNC using Putty or Minicom, simply connect to the serial (COM) port where your serial cable is connected to your TNC and follow the TNC's instructions on how to initialize it. I use 9600 baud to communicate between computer and TNC. Remember that hardware TNC's are generally old! Be gentle!

TNC's generally have 3 operating modes, COMMAND (COM), CONVERSE (CONV), and TRANSPARENT (TRANS). COM and CONV are the only ones I typically use. When you're in COM, stuff you type into Putty is interpreted by the TNC as commands. When you're in CONV, stuff you type into Putty is transmitted (either to all stations "unproto" or to the station you are connected with, with the headers automatically added by the TNC). Typing "CONV" or successfully initiating a connection to another station typically gets you from COM to CONV, and "Ctrl+C" typically gets you from CONV back to COM.

To connect to another station (such as a BBS), run "CONNECT KK6SF-1" (for the ACS BBS, or substitute whatever the desired BBS callsign and SSID is). The "-1" in this case is important to identify the BBS as opposed to other functions that may be available on that TNC; other BBS's may have other SSID's. Generally an SSID of 0 can be omitted (i.e. KJ6LDJ-0 is the same thing as KJ6LDJ). Once connected, send "H" and the BBS will send instructions for its commands. They are typically pretty consistent between BBSs (LM or LB to list my or bulletin messages, SP <callsign> or SB <callsign> to send a private or bulliten message, B for bye to disconnect, etc.).

Saturday, February 1, 2020

Kenwood TH-F6A Stuck Memory Channel

I was unable to overwrite or delete a specific memory channel. Performing a VFO Reset resolved it for some reason, as described here: https://saniac.com/unable-to-modify-or-erase-memory-channel-on-kenwood-th-f6a/

Key parts are to perform a “VFO Reset”.

  1. Power off the device
  2. Hold down [F] + Power (Display will show “RESET?” with “NO” blinking.)
  3. Turn the Tuning Control dial until the display reads “VFO RESET”
  4. Press [MNU]

Monday, August 3, 2015

First Post, Sort Of

Funny how blogs used to be huge some 10-15 years ago, via LiveJournal and others, and have now made a come-back. I guess they have their uses. Thoughts for future blogs, in no particular order:

  • Power distribution box
  • VHF/UHF vs HF
  • Outdoors stuff
  • Life
To be continued.