UGENT
High Speed Electronics
Summary
Tars Morel
6/1/2013
This is a short summary of the course High Speed Electronics, the following will sum op
everything you need to know to pass the exam, but hower more knowledge is needed to
understand this summary
CHAPTER 0:
GENERAL
Power
𝑃 = ½ 𝑅𝑒[𝑉 ∗ 𝐼 ∗ ]
Transformer
𝑉𝑙 𝐼𝑟 𝑛𝑙
= =
𝑉𝑟 𝐼𝑙 𝑛𝑟
Sinus rules
𝑠𝑖𝑛(𝑎)𝑐𝑜𝑠(𝑏) = ½(𝑠𝑖𝑛(𝑎 + 𝑏) + 𝑠𝑖𝑛(𝑎 − 𝑏))
1
1
∫ sin(𝑥)2 dx = x − sin(2x)
2
4
BJT: nonzero collector current
𝑖𝐶 = 𝐼𝐶 𝑒 𝑉𝐵𝐸 /𝑉𝑇
𝑞𝐼𝐶
𝑔𝑀 =
𝑘𝑇
Conjugate matching
Zload = Zsource*
Thevénin & Norton
gm,eff
Of CS stage
OC tau
At a capacitor the effective resistance facing it equals
rLEFT +rRIGHT + gM,EFFrLEFTrRIGHT
CHAPTER 1:
CLARIFYING CONCEPTS AND DEFINITIONS
WEAK NONLINEARITY IN THE FREQUENCY DOMAIN
N-th order harmonic distortion
Ratio of the amplitude of the n-th order harmonic to the amplitude of the fundamental
term
1-db compression point
Signal level for which the small signal gain is 1 dB lower than the law predicts
Desensitization
Presence of a strong signal decreases the gain, so a weak signal is
amplified less
Cross modulation
Cross modulation index
Strong signal with variable amplitude modulates a weak signal
Intermodulation
(IM)
Two (or more) signals with little difference in frequencies (w1 &
w2) can modulation
e.g. 2w1 – w2 or 2w2 – w1 will fall within the pass band.
3rd order interception point
3rd order input/output intercept level (IIP3 / OIP3)
Point where the first and third order harmonics have equal amplitude
DEFINITIONS AND SPECIFICATIONS IN THE TIME DOMAIN (ONLY DEFINITIONS)
Time invariant system
time shift of the input results in the same shift at the output
Memory less
 Dynamic
Output is independent of the history of the input
Linear time invariant
The output does not contain other spectral components than are present in the input
signal
Can distort the signal due to spectral limitations and possible dispersion
Inter symbol interference (ISI)
Due to spectral limitations (to steep square wave will have many harmonics => make
pulse equal to sinc) and group delay (multimode)
We can use Nyquist channeling => previous’ bit responses are zero
Elmore delay
Time that expires until the impulse response h(t) has reached its mass midpoint
Bandwidth and rise time
w3dB = t_rise*2.2
SENSITIVITY AND DYNAMIC RANGE
Sensitivity
The weakest power that van be processed with a given quality
Minimal detectable signal (MDS)
Noise factor
Ratio of input to output SNR, added noise by the system
Dynamic range (DR)
Ratio of the highest input power that can be handled with given quality (non linearity)
and the lowest input power that can be handled with a given quality (noise floor)
Spurious free dynamic range (SFDR)
Narrower than DR
Same as DR but: Minimum signal level = minimum detectable input power needed to
support a given service with a predefined quality. Maximum signal level = maximum
amplitude of a two-tone signal within the pass
band, whose IM3 products are smaller than or
equal to the noise floor. Only suitable for BW < 1
octave (else use IM2)
Can also be derived from following graph
Or
CHAPTER 2:
LINEAR CIRCUIT ANALYSIS
MATRIX REPRESENTATION: AN OVERVIEW
Linear two port network
V1, I1, V2 and I2 describe the network. Source and load.
Unilateral network
I/O ports are perfectly isolated, transmission in only one direction
Stable DC-operating point
VCE and IC
Provide DC paths via resistors where needed
Apply feedback to stabilize the operating point
Use a decoupling C (around a central frequency) at power supply
B = input, C = output, E can be both
ZIN
ZOUT
V gain
I gain
CE
Medium
Medium
-Av
-Ai
CC
High
Low
< +1
Ai
CB
Low
High
Av
< +1
SCATTERING PARAMETERS
Why scattering parameters
Z,Y,… matrices need to be terminated with incremental short or open circuit, not
possible at HF: parasitic capacitance and inductance
Each port will be terminated with a fixed and finite, high accurate impedance
Reflection coefficient or scattering parameter (Gamma)
I = Ii - Ir
V = VI + VR
I = incident: ZL = R0
R = reflected
Matched load impedance
No power reflection
Max signal source power
Source and load dissipate the same amount of power
Smith chart: Impedance chart
Zln is the normalized: ZL/R0
Loci of constant resistance
Loci of cte load reactance
TL: rotate around centre point
Smith chart: Admittance chart
Mirrored over centre point
Two port S-parameters
a = incident port power level
b = reflected port power level
All ports are terminated on R0 for measurement
Unilateral: S12 = 0
Reciprocal: S12 = S21
P gain
High
Medium
Medium
Passive (= positive energy delivered): [S]T [S]* = [E], a unitary matrix
Lossless: S is unitary
Scattering analysis of a loaded/sourced two port
GammaS = bS/aS
GammaL = bL/aL
Gamma2 = 1/GammaL
Signal flow graphs
Nodes: for every scattering variable
Branches: directed path between an a-node and a
b-bode
Node value = sum of products (arriving branch *
sourcing mode)
Signal flow graphs of a two port
Series, parallel, self-loop and splitting rule!!
Mason’s gain rule
POWER GAIN AND STABILITY
Power delivered by the two-port network to ZL
Power available from the source
Delivered when load is impedance
matched to the source
Transducer power gain GT
Power delivered by two-port to load/power available from source PL/PAVS
Operating power gain GP
Power delivered by two-port to load/power delivered by source to two-port PL/PIN
Available power gain GA
Power available at the output of the two-port / power available from source PAVN/PAVS
Unconditional stability
We consider passive terminations: |L/S | < 1
No oscillation is possible when |IN/OUT| < 1
When stability circles do not cross the
Smith chart border
Conditional stability or potential instability
Oscillation is possible but not certain
when, |IN or OUT| > 1
Range of terminations s and L for which a two
port is stable at a given frequency
Stability circle on the smith chart, locus
in L/S plane for which IN/OUT = 1
Output stability circle (& vice versa)
Defined in the output plane, describes
the stability of the INPUT network,
when gammaIN equals one