# 90 degree phase shift and frequency mixing

I intend to generate a sine wave of 14 MHz frequency ( without using LC based oscillators such as hartley or colpitt). However I only have at my disposal an op amp with GBP 3 MHz. So I plan to generate first a 500 KHz wave ( using Wien bridge oscillator probably) and step it up subsequently using mixers.

Firstly, is there a better alternative to generate 14 MHz( again not using LC based oscillators) ?

Also, I require the 14 MHz wave to be phase shifted by 90 degrees. Again due to lack of components, I can only use the same op amp and realize an integrator or differentiator for phase shift.

Now here is the important question :

Are phase shifting and Mixing commutative ?

That is, can I first phase shift the 500 KHz wave and then subsequently mix it to increase frequency to 14 MHz or do I have to first mix and then apply shift at last ( which obviously I cant) ?

If they are, then what other things do I need to consider in this operation ?

• To educate myself a bit, why can you not mix and then shift? Commented Jul 14, 2014 at 17:50
• Well, because of availability of components as I mentioned, my integrator or differentiator would not work at high frequency. Commented Jul 14, 2014 at 18:16
• Why can't you use colpitts or hartley? Commented Jul 14, 2014 at 18:29
• If you can't get a simulation of a colpitts to work then I have little faith in believing you'll get anything else to work. So you want 14MHz by stepping up 500kHz but this is wrong the way you say because it'd need to be one-sixteenth of 14MHz? Colpitts are easy - are you sure you didn't wait sufficient time for the oscillator to start building up it's amplitude? Commented Sep 12, 2014 at 21:58
• Show the circuit dude. I've used single BJT colpitts with varactor tuning tons of times from 20M to over 400M and they all start within 1 milli second in reality and simulation. Dunno what you doing wrong but DDS is a good solution if you can't be bothered. Commented Sep 13, 2014 at 0:47

What is your application? From what you've mentioned so far, I'm going to go out on a limb and say that it sounds like you're trying to build a 14MHz local oscillator for a quadrature mixer/detector in the ham radio 20 meter band, so I'll address some issues specific to that application (though these issues are not exclusive to that application).

First, to answer your question, you'll want to get the 14MHz signal generated first, then apply the 90 degree phase shift. There are a couple of reasons for this, including, but not limited to:

1. Once you have your in phase ("I", aka, not-phase-shifted) and quadrature ("Q", aka, 90 degree shifted) signals, you now have two separate signals, so if you want to take a 500kHz signal and use mixers to multiply it up to 14MHz, you now have to have two mixer chains, one for each signal.
2. Your two mixer chains now have to be identical in every respect in order to ensure that no additional phase changes occur between your I and Q signals. Physics/murphy make this difficult.

So, it's easier and more practical to do the phase shift last. Since it sounds like you just need a fixed-frequency oscillator, this can be done pretty simply with passive components; see figure 6 (and the corresponding text) from this ARRL article.

You could also use a pair of D-type flip flops to generate your I and Q signals, which would work over a wide range of frequencies, but it requires your oscillator to be running at 14*4 = 56MHz; there's an example of this in the "Generating I/Q Quadrature Local Oscillator Signals" section of this page.

Now, even if you did one of the above and got your 14MHz I and Q signals generated, I think you would not be very happy with the result. Although you didn't mention it, from your description I'm guessing that your 500kHz op-amp oscillator is some form of RC relaxation oscillator? Those have terrible frequency stability (with respect to, say, a crystal oscillator), and to make matters worse, multiplying the signal up also multiplies the frequency instability!

Likewise, specially WRT local oscillators, phase noise is very important; multiplication of a signal will increase (worsen) the phase noise by a factor of 20*log(N), where N is the multiplication factor. Without going into too much detail on phase noise, as with most forms of noise, less is generally better.

So, given the fact that it sounds like you need a fixed-frequency oscillator on/around 14MHz, I would strongly recommend building a crystal oscillator. The Pierce oscillator design is particularly popular, as it is hard to beat in terms of simplicity and performance. You can use a jellybean transistor (e.g., 2N3904) for the amplifier, or use an inverting logic gate IC; there is a related question here which may help you get started; you can then do either a passive/active phase shift circuit, as mentioned above, to get your I and Q signals.

BTW, if my hunch about your application is correct, I suspect your comment "I'm afraid it has to be a sinusoid" is probably incorrect. Most mixers actually work better with square wave LO input, as it switches the mixer's diodes/transistors on faster.

Can it be a square wave?
Maybe crystal oscillator. Or a RC plus digital inverters.

For the transistor oscillators, and simulation. It's sometimes hard to get the oscillators going in spice. I'm not a spice expert, but I sometimes give the oscillators a "bump" to get them started.
(hit 'em with a one time pulse/ square wave.)

And if that doesn't work try soldering up the circuits.
Reality rules over simulation. (solder is Bob Peases favorite programming language :^)

I don't think you'll have much luck getting to 14 MHz from 500 kHz, that's going to be about 5 doubling steps.

• I'm afraid it has to be a sinusoid. All I want to know is are mixing and phase shifting independent of the order in which they are done or not ? Commented Jul 14, 2014 at 19:42
• Ah, well the phase shift depends on the frequency, and mixing changes the frequency.. it gets a bit complicated. I'd try the transistor circuits again. Commented Jul 14, 2014 at 20:45
• I think the output phase of a mixer is equal to the phase delta between the two inputs. This is only valid when referring to a single mixer element. For example, an image reject mixer contains multiple mixing elements, along with other stuff. Commented Sep 13, 2014 at 4:51