Frequency Upconversion and Downconversion ELEC 433 - Spring 2013 - - PowerPoint PPT Presentation

Frequency Upconversion and Downconversion

ELEC 433 - Spring 2013 Evan Everett and Michael Wu

Transmit Chain

Data

∼ ∼ ∼

D/A

∼ ∼ ∼

Baseband Upconversion RF Upconversion

RF Up/Downconversion

• Purpose:
• Baseband is great for processing
• RF better for propagation

XC(f)

fC

−fC

X(f)

Baseband Tx Processing Baseband Rx Processing RF Channel

X(f)

RF Upconversion

• Goal: Convert complex I/Q samples at baseband

to real signal centered at carrier

• Strategy: shift in frequency is multiplication by

sinusoid in time:

• Remember the reality condition: If is real

then x(t)

X(−f) = X∗(f)

X∗(f + fC)

X(f − fC)

x(t)ej2πfct ↔ X(f − fC)

XC(f)

fC

−fC

X(f)

RF Upconversion

Briefly discussed in Modulation lab: Text

RF Upconversion

xI(t) xQ(t) cos(2πƒct)

• sin(2πƒct)

xc(t)

RF Upconversion

xI(t) xQ(t) cos(2πƒct)

• sin(2πƒct)

xc(t)

x(t) = xI(t) + jxQ(t)

X(f)

XC(f) = X∗(f + fC) + X(f − fC)

X∗(f + fC)

X(f − fC)

XC(f)

fC

−fC

xC(t) = xI(t) cos(2πfCt) − xQ(t) sin(2πfct) = |x(t)|cos(2πfCt − ∠x(t)) = Re[x(t)ej2πfCt]

RF Downconversion

• Goal: Convert real-valued signal at carrier to I/Q

samples at baseband

• Strategy: shift (multiply by sinusoid) and filter

1) Shift by ƒc by multiplying by a complex sinusoid

xc(t)ejπfct

XC(f)

fC

−fC

2fC 2fC

2) Lowpass Filter to remove high frequency content

RF Downconversion

X(f)

cos(2!ƒct) sin(2!ƒct) LPF LPF xI(t) xQ(t) xI(t) xQ(t) cos(2!ƒct)

• sin(2!ƒct)

xc(t)

Source I/Q signals Channel-ready signal Recovered I/Q signals

RF Up/Downconversion

XC(f)

fC

−fC

X(f) 2fC X(f)

Transmit Chain

Data

∼ ∼ ∼

D/A

∼ ∼ ∼

Baseband Upconversion RF Upconversion

• WARP radios implement RF upconversion and

downconversion for us

Transmit Chain

Data

∼ ∼ ∼

D/A

• WARP radios implement RF upconversion and

downconversion for us WARP Radio

Baseband Upconversion

• This week you will be implementing digital

baseband up/downcoversion

Baseband Up/Downconversion

• Goal: shift I/Q samples away from DC
• Difference from RF upconversion: output is still

complex (I/Q) Radio

I Q

• Reason: most radios reject DC input due to an

RF issue called DC offset (a.k.a. carrier leakage)

AC coupled I/Q inputs

Baseband+RF Upconversion

DC

fIF

IF

! fRF

fIF

RF

via FPGA via Radio

• Radio’s usable input spectrum has a notch at DC
• Shift I/Q samples to an intermediate frequency

Baseband Up/Downconversion

xI(t) xQ(t) cos(2!ƒct) sin(2!ƒct) cos(2!ƒct)

• sin(2!ƒct)

xI(t) xQ(t) upconverted xI(t) upconverted xQ(t)

Complex Multiplication Complex Multiplication

fIF

A Few Complications

• Desired symbol rate = 5 Mhz, DAC sample clock = 40Mhz
• Before upconversion, upsample I/Q signals by 8 then filter (we

know how to build efficient interpolaters).

• Do opposite on the receiver side.
• Delay between Tx and Rx: what if the receiver starts listening

after a transmitter begins sending?

• Tx/Rx carrier frequency mismatch: residual frequency left at

receiver

xI(t) xQ(t) cos(2!ƒct) sin(2!ƒct) cos(2!ƒct)

• sin(2!ƒct)

xI(t) xQ(t) upconverted xI(t) upconverted xQ(t)