I think this scheme will do what you want. First, download this circuit of a TDA7000 radio.
http://schematiccircuit.com/fm-radio-ic ... ose_buttonIf you click on the circuit it will enlarge to a useful size. Make it and run it from a 9V supply (stabilized because the varicap is voltage sensitive). In spite of what I said earlier about removing the de-emphasis cap on pin2, a pulse will normally equate to a low frequency audio signal so it can be left in.
When you have got it going, adjust the 100K pot to tune 88MHz and make a note of the reading on the slider of the pot relative to 0V. Do the same for 108MHz.
For the ‘sweeper’, see the attached circuit.
Here is how it works. IC1 is wired as an astable oscillator. Its output is not used. C1 charges from 3V to 6V by the current through Tr1 in a time of about 200mS. When the voltage on pin6 reaches 6V, pin7 discharges C1 very quickly until the voltage at pin2 gets down to 3V then the cap starts to charge again. The result is a sawtooth waveform of 3Vpp.
This paragraph describes the linear drive for the sweep that changes the ramp voltage at a linear rate. Here’s how that bit works.
Tr1 is a current source circuit that feeds C1 with a constant current – whatever its state of charge. That ensures the sweep is linear. Tr1 is biased through R1 and D1 and D2 conduct, so the bias will be a constant 1.4V and the voltage across R1 will always be 0.7V. That gives a constant current through the emitter and collector that charges C1 linearly. I am not sure how much that will affect the linearity of the frequency sweep, so you can leave those components out if you like and just put a 50K preset resistor between pin2 of the 555 and the 9V rail instead.
Now for the rest. The 3Vpp sawtooth is fed to an inverting amplifier to amplify the sweep. The output sawtooth amplitude will be 3V x VR2/R3. In the event that you measured earlier are less than the 3V span of the sawtooth, I will alter the circuit to give a reduction.
The ‘centre scan’ voltage is set by VR1. So to set the controls up, adjust VR1 until the voltage on its slider is the average of the two varicap voltages that you measured earlier. Then adjust VR2 so that sweep spans the voltages you recorded earlier. Then disconnect the 100K pot feeding the varicap and connect the op-amp output to where the slider was.
If you have any queries, please ask.
Happy building.
(Edit 06/10) Make sure the op amp is able to input down to zero volts level. Use a CA3140 or similar.