The Expo 100 kit type "A" or "A+" works by injecting a crystal frequency into a mixer chip in the radio's PLL. The mixer chip's output feeds into the PLL input. Has a crystal for each new band, and a one-transistor oscillator circuit.
Pin 4 of the mixer chip has 15.36 Mhz coming from a single slug-tuned coil that has a 5.12 MHz 5-Volt square wave feeding into it. This gets you a half-Volt or a Volt of the third harmonic, 15.360 MHz.
The Expo kit has a crystal oscillator with an output level several times the level of the radio's internal 15.36 Mhz source.
The Expo kit's output overpowers the PLL input, moving all 40 channels up or down. The radio's stock 15.36 MHz signal is still there at pin 4 of the TA7310 mixer chip, but the stronger level from the Expo kit drowns it out. The PLL locks to the stronger one.
To go 45 channels up, the crystal is 15.810 MHz. Down 45 is 14.91 MHz.
The Expo kits were sold and designed before the first "export" radios showed up. Those radios move 45 channels per band, so that the lower band gives you 26.955 on channel 40, and the upper band starts at 27.415 on channel 1.
But the original Expo kits only moved you up or down 44 channels. This caused channel 1 to show up twice. Once where it should be, and again with the selector on 40 with the lower band selected.
Likewise, channel 1 on the uppers wasn't channel 41, it was channel 40.
Not sure why they were built with overlap. When they hit the market, nobody cared.
Later "A" and "A+" kits used a dirty trick to get that '45 channel' jump from the same, old crystals. Must have figured it would sell better if the channel display on your Cobra 29 would read the same lower channels as your buddy's Galaxy.
They put a disc capacitor in parallel with the lower-band crystal to pull it down from 14.92 to 14.91 MHz
And they put a capacitor in series with the upper-channel crystal to pull it up from 15.80 to 15.81 MHz.
Just one problem. This screwed up the feedback in the crystal oscillator circuit. It would reduce the output so much that a radio might "kick in" and get the lower channels when selected, then randomly "kick back" to the normal 40 channels as the radio warmed up. If the output level from the Expo kit isn't big enough, the PLL may have trouble making up its mind which one it will lock onto.
Using the old crystals was probably a LOT cheaper than getting new ones made.
One of these days, someone needs to find a copy of the original early-80s instruction sheet. Shows the correct hookup for the "A" kits. Any newer instructions that show the white wire connected to one pin of a tuneable coil are just wrong.
73