# RF circuit parameters

1. Jul 13, 2012

### akb11

I read that conventional (low frequency) circuit parameters - voltage gain and power gain are not applicable for RF circuits but I didn't understand why?

2. Jul 13, 2012

### yungman

In RF design, Smith Chart is the utmost important thing. It presents information as reflection and impedance.

1) In RF, parasitic capacitance and inductance come into play, it gets complicated if you use conventional representation.

2) In RF, the component dimension is comparable to the wave length of the frequency, the conventional circuit schematic model start to fall apart. You have to use phasor representation for everything.

3) Impedance matching for maximum power transfer is of utmost importance. S-parameters are used as they are power waves. Also with that plotting on Smith Chart, you get the input, output impedance. With that, you design the matching network.

RF is not that intuitive, it is my opinion that you better off think in Smith Chart. I always joke about dancing on the Smith Chart!!! It is like design using Bode plot for low frequency circuit, except Smith Chart provide a lot more information, much less intuitive. You even plot stability circle to avoid stepping into "land mind" where it get unstable. You also design filters by moving the quality factor plot on the chart.

4) As you take parasitic into account, the input and output impedance change with frequency, you cannot use a single value of the parameters to design, you have to design for specific frequency.

3. Jul 14, 2012

### akb11

Hi ,

Thanks for your reply. I went through Smith Chart and also tried a couple of impedance matching exercises. I have understood when to use a series L or C and when to use a parallel L or C.

So just to check if i have understood it right.
In RF circuits we use insertion voltage gain instead of the usual voltage gain. In low frequency circuits, the source voltage is always equal to voltage at the device (2 port network) input. In RF circuits, the voltage transfer from source to device input depends on the impedance match and in the best possible case ( i.e. reflection coefficient is 0 ) only half of the source voltage appears as device input voltage or half of the power is transferred from source to input (Maximum power transfer theorem).

Have I understood it correctly ?

4. Jul 14, 2012

### sophiecentaur

You can use many different circuit parameter systems of RF. S parameters have an advantage in that they describe how a device will work in a standard (normally 50Ω) transmission line system. S parameters are easy to measure with the device inserted into a 50Ω system and allow you to predict the behaviour when multiple devices are cascaded. They are ideal for UHF and microwave circuit testing and design but not so handy for lower frequency devices in which feedback is used (afair).

5. Jul 14, 2012

### yungman

I was going to come back and stress some points relate to what you brought up here.

1) Gain in RF is hard to come by, mainly because the input impedance that people usually assumed to be high is not so in RF. This is because the parasitic capacitance pretty much dominates the input, the lead inductance of the bonding wire(s) also play a major role. That's the reason if you look at the S11 ( that show input impedance) plot on the Smith chart, it goes quite a bit below 50Ω. So you need power to drive the transistor/amplifier. You don't get gain like normal common emitter stage in low frequency. So.......Power is expensive, you can't afford to lost efficiency due to mismatch.

2) We don't use voltage gain in RF because more voltage don't mean more power transfer. Remember W=IV. S parameters are power waves. We optimal power transfer, not voltage transfer like the low frequency circuits. If you study Phasor, you can see if you terminate with open circuit, you get max voltage, but you don't transfer power.

3) In low frequency circuit, the parasitic capacitance and inductance is negligible, so the parameters remain quite constant. But in RF, the parasitic dominates and they are frequency dependent. That's the reason you have a long list of S parameters for all frequency points.

4) Remember also the physical dimension. When the dimensions are comparable to the wave length ( λ/4), things behave very differently. In low frequency model, you assume the λ>>>physical dimension.

If you get rid of the parasitic and physical dimension limitations, the RF device is no different from the low frequency device. All the S parameters at different frequencies become constant and the low and high frequency model become the same. There is no mystery in this, RF parameters just take the parasitic and physical dimension into account.

I can't speak for mm wave stuff, but for a few GHz RF, there is no black magic, it's just taking into consideration of all the physical dimensions and parasitic parameters. Spend the time "dancing" on the Smith chart. I've seen RF engineers taking a short cut, relying on application circuits provided by manufacturers and blindly copy the circuit. That's the reason why application schematics become so important now a days.

Last edited: Jul 14, 2012
6. Jul 14, 2012

### vk6kro

2) We don't use voltage gain in RF because more voltage don't mean more power transfer. Remember W=IV. S parameters are power waves. We optimal power transfer, not voltage transfer like the low frequency circuits. If you study Phasor, you can see if you terminate with open circuit, you get max voltage, but you don't transfer power.

Often in a receiver, you start with a signal of a few microvolts from an antenna and this has to end up providing several volts to a speaker.
So, that is a voltage gain of about a million and much of it has to be RF gain.

Or, in a transmitter, you start with a hundred millivolts out of a crystal filter and this has to become 100 volts across the input terminals of an antenna.
This is a voltage gain of about 1000.

So, I think you would have to give the context when making a statement like that.

7. Jul 14, 2012

### yungman

I guess I should not have said voltage gain don't mean anything. Instead I should concentrate on power gain. Power gain in certain sense is related to voltage gain, but in a lot of sense it's not.

Voltage gain is not direct relate to power gain, if you have a device that has higher input impedance, and has lower output impedance, you can get power gain, but if you straightly measure the voltage, the input voltage can be higher than the output voltage at the device even though you have power gain. If you measure the voltage and compare at the input of the input matching network and the output of the output matching network, where both are 50Ω, then voltage gain is much more useful.

RF circuit is like there is a transformer between each stage to match the output impedance of the the first device to the input impedance of the next device and so on. If you have step up or step down transformer on every step, voltage gain don't mean a whole lot until you take into the context of the impedance. The passive matching network can have voltage gain/attenuate like transformer.......it is really like a transformer. The difference is for conventional transformer, you really only match "real" impedance. Where is the RF matching network, we match the complex conjugate impedance of the stages. That's the reason people mostly use power gain in the RF chain.

Last edited: Jul 15, 2012
8. Jul 18, 2012