# Can an inductor/capacitor/resistor combo emit the same frequency as a given crystal oscillator?

Beginner in electronics and radio frequencies in particular interest me. That said I'm having trouble understanding what components are used when. When I initially searched about radio frequencies, most knowledge articles said those frequencies are produced based off of a crystal oscillator that'll oscillate at a specific frequency.

However, in some DIY FM transmitter tutorials I've looked at a lot of the circuits don't incorporate any crystal. Rather, the circuits incorporate certain capacitors, and a coil (inductor?).

In this case are they doing more or less the same thing? For example, if I had a crystal oscillator generating a frequency at 88.1 MHz.. could I create an equivalent circuit using capacitors & a coil that also produces an 88.1 MHz signal? If no, why not? If yes, is there a reason to use one over the other?

Appreciate any responses.

• Not over the same temperature range. – Ignacio Vazquez-Abrams Mar 20 '17 at 0:46
• That's interesting I haven't read much about temperatures in circuits yet. Shot in the dark here, but would the capacitor/inductor combo tend to be hotter than a crystal oscillator conunterpart? – LJR135 Mar 20 '17 at 1:10
• The frequency of a capacitor/inductor oscillator will vary with temperature (and other things) much more than a crystal-controlled oscillator. Generally, crystal-controlled oscillators are used when you want a fixed frequency. LC oscillators are used when you want a variable-frequency oscillator. – Peter Bennett Jun 15 '18 at 5:35

Yes, you can build a oscillator with inductors and capacitors that will have the same frequency as your crystal oscillator. Using inductors and capacitors, you can reach frequencies much higher or much lower than you can reach with crystal oscillator.

The reason why crystal oscillators are used is because they have a much better frequency stability. Frequency stability does not matter much for an experimental DIY toy FM transmitter, but it does matter for many other uses.

• Great thank you for the response! In that case for my home DIY I'll probably just go with an inductor/capacitor circuit. Just another follow-up out of interest, is there a way to reach higher frequencies with crystal oscillators? – LJR135 Mar 20 '17 at 1:04
• There are some circuits that can be used to “multiply” a frequency. They use a phase-lock loop. – user2233709 Mar 20 '17 at 1:10
• Thanks for all your help. Took a look at some lessons about it and it seems a bit too advanced given my knowledge but none the less interesting. Cheers! – LJR135 Mar 20 '17 at 1:32

Crystal oscillators are nice if you want to broadcast from a precise frequency. You may achieve the same goal with a coil & capacitor (called an LC tank circuit). Probably in the circuits you have seen so far utilizes this tank circuit, with their values chosen to resonate at your preferred frequency. It is all nice with capacitors, but most of the time, you may not be able to find a good inductor, so you will have to wind it by yourself. However, I know of no way to measure the inductance without the help of at least a frequency generator. So you may follow a tutorial, wind up your own air core inductor, and it may still not work. And you cannot be sure if the fault is inductor related or something else. Crystal oscillator saves you from this pain.

• Thanks for the response, that's a good point and something I'd wondered about. The tutorials I've looked at all details winding some wire around a screw to create the coil, but none of them talk about what actually determines the frequency output. My guess is it's the distance between each individual coil that will determine the frequency? – LJR135 Mar 20 '17 at 17:33
• @Lester it has a formula, based on the coil diameter, wire length, wire gauge etc... you can find air core inductor calculators online, however they differ between each other for some unknown reason... so you may never find the real inductance value. – C K Mar 20 '17 at 17:39
• @Lester About the frequency, you probably saw it, if you didnt you can see it searching "lc circuit resonant frequency". It is found by equalizing the reactances of L and C. – C K Mar 20 '17 at 17:47

An oscillator is an amplifier with positive feeback, and a "frequency determining element". This can be a crystal, or an LC resonant "tank". The LC oscillator isn't usually stable enough for most applications. Here is what typically happens when you build your first LC oscillator.

First, the mechanical properties of the tuning element (usually a variable capacitor) are such that after you adjust it, it "relaxes" slightly, causing the frequency to change. So you end up adjusting it past the desired frequency, and letting it "settle" back to the target frequency.

Next, you find that as you move your hand away from the circuit, the frequency changes again. The stray capacitance added by your body affects the frequency. You end up moving your hand towards or away from the circuit in order to keep it on frequency. Next, you find that even if you hold your hand steady, the frequency is drifting and you have to move your hand again to correct for this. This drift may be from a change in temperature, voltage, or more mechanical changes.

So, the answer is "yes", but you eventually realize life might be a lot easier if you used a crystal. Crystals aren't perfect, but they are magnitudes better. They also require less power to keep the oscillations going. Good LC oscillators can be built; they will feature a well-regulated voltage supply, rigidly mounted components, and a metal shield enclosing the circuit. There will also be temperature compensation (or temperature control).

There were some remarks about frequency multiplication. This could be accomplished by introducing distortion into the oscillator, which produces harmonics. Then, another LC tank circuit is tuned to a harmonic of the original frequency. Another amplifier may be used to boost the resulting signal. This is how it was done in the days of pure analog circuitry.

• Thanks for the response. It certainly sounds like using a crystal is much simpler for a beginner than an LC tank circuit. I'll probably end up doing both out of interest. Using a crystal it does sound like I'll have to learn more about frequency multiplication/PLL though before I can generate something within that FM range. Eventually I'd like to incorporate in my Arduino and some other components, but only after I've gotten a good understanding of the topic and manage to generate a frequency. – LJR135 Mar 20 '17 at 18:19

Time to bring servo-loops or negative-feedback into your skillset.

OpAmps are examples of negative-feedback, to achieve precise ratios of voltage-gain. The key bit of math, given G = opamp openloop gain, H= the feedback ratio:

$$Avcl = G/(1 + G*H)$$

defines the input/output ratio(gain). Huge G values -> very precise gain.

simulate this circuit – Schematic created using CircuitLab

We use the same feedback methods, but instead of making voltages be a precise ratio, we make the ratio of zero-crossings a precise ratio, using FlipFlops and an Edge_Comparison box, the PhaseFrequencyDetector:

The VCO (the 16MHz +-1Mhz) might be 7MHz to 89MHz, but the Phase Frequency Detector ---PFD--- will handle that enormous range, even as the inductors and capacitors and transistors (providing power gain, so the LCs will have a growing amplitude, required by an oscillator) change properties over temperature and with VDD and simply because inductors and capacitors are never exact. A proper PFD is a very interesting beast, and as long as the oscillator is oscillating (some stop oscillating if the VTUNE is requesting too high a frequency) and the PFD functions over the entire range of the VCO, the UP and Down pulses push the VTUNE[the control voltage out of the 2C/1R filter] to the needed voltage; simply by comparing the timing of edges, this feedback system performs frequency lock and phase lock.

Key to precise frequency ratio is the charge-storage performed by C1. Any residual error, caused by slight up/down charge imbalance, caused by the 8th edge out of our 1/2*1/2*1/2 divider not exactly aligning with same polarity edge from the Fref, will build up and up (or down and down) on C1, even if just tiny charges. Thus over time, the 8th edge from the variable-oscillator is more and more exactly aligned with Fref from the crystal reference.

• Thank you for the detailed response. The graphics help me a lot as well in understanding. Cheers! – LJR135 Mar 20 '17 at 19:46
• Isn't this just a phase-locked loop? – Scott Seidman Mar 22 '17 at 17:00

The crystal is at least much easier if you need a precise frequency. Tuning an LC group and keeping it stable if the environment changes is an annoying task. You can get both in the same frequency range (crystals can be bought off the shelf in 100+ MHz which would be right in your FM range) On the other hand, if you really intend to produce FM radio signals, the LC group might be the better way because, contrary to a crystal, an LC group can be easily (de)tuned via a capacitive diode or similar methods, which makes it quite easy to modulate your frequency. A crystal will oscillate at its cut frequency and not far outside of that, so it's better suited for applications that require stability, like for clock generation.

If you seek a working oscillator, avoiding a circuit that just sits there quietly, consuming power but NOT OSCLLATING, then read up on Barkhausen's work.

He offers 2 criteria: (1) you need power gain, at the desired frequency (often stated as voltage gain) (2) you need exactly N * 360 degrees phaseshift, at the desired frequency; note that bit of math allows 0 degrees, 360 degrees, 720 degrees

I've read papers suggesting "too much power gain" will prevent oscillation. That was stated as "high gm (transconductance, output amps per input volt) will prevent oscillation".

In reality, at "high gm" (strong drive strength), the loop was not reaching that Zero Degrees phaseshift condition, because the R became too low.