Is there sth wrong with this quadrature downconversion?

[cmosbjt]

**broken link removed**

I think there is sth wrong. Do you think so?

 

[nand_gates]

I dont see anything wrong in this.. It looks perfectly OK....
Can you tell whats ur guess what's wrong???

 

[cmosbjt]

Is the output signal wrong?

If the input signal is a(t)cos(ωt+Θ)+b(t)sin(ωt+Θ), then the I/Q output should be:
I --> a(t)cosΘ + b(t)sinΘ
Q--> -a(t)sinΘ + b(t)cosΘ

If the input signal is a(t)cos(ωt+Θ) to the upper branch and b(t)sin(ωt+Θ) to the lower branch, then the I/Q output should be:
I --> a(t)cosΘ
Q--> b(t)cosΘ

This graph is from Razavi RF Microelectronics, P129.

Correct me if I am wrong, thanks.

 

[dsjomo]

I think you are right, something wrong in this figure.

 

[DonJ]

It's a confusing picture where the author tried to imply a complex input signal.

 

[nand_gates]

Yep!!
The i/p should have been written as
a(t)cosΘcos(ωt) + b(t)sineΘsine(ωt) Which is mathematically correct
But here we are only interested in frequncy domain analysis, we need to
show frequency translation hence in the diagram i/p is shown as
a(t)cos(ωt+Θ) + b(t)sine(ωt+Θ) which is not mathematically correct

 

[DonJ]

Comlex signal processing should be done in the complex domain. Confusing otherwise ...

 

[cmosbjt]

Yep!!
The i/p should have been written as
a(t)cosΘcos(ωt) + b(t)sineΘsine(ωt) Which is mathematically correct
But here we are only interested in frequncy domain analysis, we need to
show frequency translation hence in the diagram i/p is shown as
a(t)cos(ωt+Θ) + b(t)sine(ωt+Θ) which is not mathematically correct

Sorry, I do not get your point. Can you explain more detail?
Thanks.

 

[biff44]

I do think there is something wrong with the original diagram. It shows two sigals linearly adding at the input, but they are of the same frequency! So there is no difference in these two signals in the frequency domain, so using a mixer and filter is no longer going to seperate the two signals at the outputs.

If the input signal were comprised of two signals at different frequencies (spaced farther apart than 2 X lowpass filter cuttoff), then the block diagram starts to make some sense.

 

[DonJ]

biff44,

The author should have operated in the complex signal domain.

 

[sanim]

Really Razavi says about digital modulation (p.128). For this reason the picture is not correct. Output of digital modulator in common case is described as a(t)cosΘcos(ωt) - b(t)sineΘsine(ωt) (thanks to nandgates for formular). If we can neglect amplitude mismatch, a(t) = b(t), then input signal is a(t)cos(ωt+Θ). And no complex signals.
Regards.