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EIE 211 Electronic Devices and Circuit Design II. EIE 211 : Electronic Devices and Circuit Design II Lecture 9: Two-port Networks & Feedback. EIE 211 Electronic Devices and Circuit Design II. Example : Design a 2 nd order high pass active filter based on the inductor - PowerPoint PPT Presentation
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04/19/2023 1 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
EIE 211 : Electronic Devices and Circuit Design IILecture 9: Two-port Networks & Feedback
04/19/2023 2 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Example: Design a 2nd order high pass active filter based on the inductor replacement
04/19/2023 3 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Second Order Active Filters based on the Two-Integrator-Loop Topology
To derive the two-integrator loop biquadratic circuit, or biquad, consider the high-pass transfer function
We observe that the signal (ωo/s)Vhp can be obtained by passing Vhp through an integrator with a time constant equal to 1/ωo. Furthermore, passing the resulting signal through another identical integrator results in the signal (ωo
2/s2)Vhp. The block diagram on the next page shows a two-integrator arrangement.
04/19/2023 4 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
From
It suggests that Vhp can be obtained by using the weighted summer in Fig b. Now we combine blocks a) and b) together to obtain:
04/19/2023 5 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
If we try to look at the Fig c. more carefully, we’ll find that
22
2
)/( ooi
hphp Qss
Ks
V
VT
And the signal at the output of the first integrator is –(ωo/s)Vhp, which is a band-pass function, with the center-frequency gain of –KQ,
Therefore, the signal at the output of the first integrator is labeled Vbp. In, a similar way, the signal at the output of the second integrator is (ωo
2/s2)Vhp, which is a low-pass function,
Thus, the output of the second integrator is labeled Vlp. Note that the dc gain of the low-pass filter is equal to K. Hence, the 2-integrator-loop biquad realizes 3 basic 2nd order filtering functions simultaneously, that’s why it’s called a universal active filter.
04/19/2023 6
EIE 211 Electronic Devices and Circuit Design II
Circuit ImplementationWe replace each integrator with a Miller integrator circuit having CR = 1/ωo and we replace the summer block with an op amp summing circuit that is capable of assigning both positive and negative weights to its inputs. The resulting ckt, known as the Kerwin-Huelsman-Newcomb or KHN biquad.
04/19/2023 7 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
We can express the output of the summer Vhp in terms of its inputs, Vbp = –(ωo/s)Vhp and Vlp = (ωo
2/s2)Vhp, as
To determine all the parameters, we need to compare it to the original eq:
We can match them up, term by term, and will get:
04/19/2023 8 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
The KHN biquad can be used to realize notch and all-pass functions by summing weighted versions of the three outputs, LP, BP, and HP as shown.
Substitute Thp, Tbp and Tlp that we found previously, we’ll get the overall transfer function
from which we can see that different transmission zeros can be obtained by the appropriate selection of the values of the summing resistors. For instance, a notch is obtained by selection RB = ∞ and
04/19/2023 9 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Two-Port Network Parameters
04/19/2023 10 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Characterization of linear, two-port networksBefore we begin a discussion on the topic of oscillators, we need to study feedback. However, in order to understand how the feedback works, we also need to first learn the two-port network parameters.
A two-port network has four port variables: V1, I1, V2 and I2. If the two-port network is linear, we can use two of the variables as excitation variables and the other two as response variables. For example, the network can be excited by a voltage V1 at port 1 and a voltage V2 at port 2, and the two current I1 and I2 can be measured to represent the network response.
There are four parameter sets commonly used in electronics. They are the admittance (y), the impedance (z), the hybrid (h) and the inverse-hybrid (g) parameters, respectively.
04/19/2023 11 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Two-Port Network (z-parameters)(Open-Circuit Impedance)
2121111 IzIzV
2221212 IzIzV
021
111
II
Vz
012
112
II
Vz
Open-circuit input impedance
At port 1
Open-circuit reverse transimpedance 012
222
II
Vz
021
221
II
Vz
At port 2
Open-circuit forwardtransimpedance
Open-circuit output impedance
V1
+
I1
V2
+
I2
z11z22
z12I2 z21I1+ +
2
1
2221
1211
2
1
I
I
zz
zz
V
V
04/19/2023 12 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
04/19/2023 13 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Two-Port Network (y-parameters)(Short-Circuit Admittance)
2121111 VyVyI
2221212 VyVyI
021
111
VV
Iy
012
112
VV
Iy
Short-circuit input admittance
At port 1
Short-circuit reverse transadmittance 012
222
VV
Iy
021
221
VV
Iy
At port 2
Short-circuit forwardtransadmittance
Short-circuit output admittance
V1
+
V2
+
I1 I2
1/y11 1/y22
y12V2 y21V1
2
1
2221
1211
2
1
V
V
yy
yy
I
I
04/19/2023 14 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
04/19/2023 15 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Two-Port Network (h-parameters)(hybrid)
2121111 VhIhV
2221212 VhIhI
021
111
VI
Vh
012
112
IV
Vh
Short-circuit input impedance
At port 1
Open-circuit reverse voltage gain 012
222
IV
Ih
021
221
VI
Ih
At port 2
Short-circuit forwardcurrent gain
Open-circuit output admittance
V2
+
I2
1/h22
h21I1
V1
+
I1
h11
h12V2 +
2
1
2221
1211
2
1
V
I
hh
hh
I
V
04/19/2023 16 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
04/19/2023 17 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Two-Port Network (g-parameters)(inverse-hybrid)
2121111 IgVgI
2221212 IgVgV
021
111
IV
Ig
012
112
VI
Ig
Open-circuit input admittance
At port 1
Short-circuit reverse current gain 012
222
VI
Vg
021
221
IV
Vg
At port 2
Open-circuit forwardcurrent gain
Short-circuit output impedance
V2
+
I2
g22
g21V1
V1
+
I1
1/g11
g12I2 +
2
1
2221
1211
2
1
I
V
gg
gg
V
I
04/19/2023 18 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
19
EIE 211 Electronic Devices and Circuit Design II
z-parameter examplesI1 I2
V1
+ V2
+6
I1 I2
V2
+V1
+
12
3V2
+V1
+
I1 I2312
6
30
012
00
00
312
21
221
12
112
2211
Z
II
VZ
II
VZ
ZZ
66
66
60
60
66
21
221
12
112
2211
Z
II
VZ
II
VZ
ZZ
96
618
66
0
66
0
918
1
1
21
221
2
2
12
112
2211
Z
I
I
II
VZ
I
I
II
VZ
ZZ
Note: (1) z-matrix in the last circuit = sum of two former z-matrices
(2) z-parameters is normally used in analysis of series-series circuits
(3) Z12 = Z21 (reciprocal circuit)
(4) Z12 = Z21 and Z11 = Z22 (symmetrical and reciprocal circuit)
04/19/2023 20 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
y-parameter examples
I1 I2
V1
+ V2
+
0.05S
V2
+V1
+
I1 I20.2S0.1S
0.025S
05.005.0
05.005.0
05.005.0
0
05.005.0
0
05.005.0
1
1
21
221
2
2
12
112
2211
y
V
V
VV
Iy
V
V
VV
Iy
ySy
S
S
S
0769.00615.0
0615.00692.0
S0615.0 ,reciprocalBy
S0615.0
0615.08.0025.01.0
0769.0But
0
S0769.0025.01.0
1
2.0
1
S0692.0025.02.0
1
1.0
1
1221
12
221
121
22222
12
112
1
22
1
11
y
yy
y
VII
III
VVyI
VV
Iy
y
y
04/19/2023 21 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Example: figure below shows the small-signal equivalent-ckt model of a transistor. Calculate the values of the h parameters.
04/19/2023 22 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
04/19/2023 23 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Summary: Equivalent-Circuit Representation
04/19/2023 24 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Feedback
04/19/2023 25 King Mongkut’s University of Technology Thonburi
Feedback
What is feedback? Taking a portion of the signal arriving at the load and feeding it back to the input.
What is negative feedback? Adding the feedback signal to the input so as to partially cancel the input signal to the amplifier.
Doesn’t this reduce the gain? Yes, this is the price we pay for using feedback. Why use feedback? Provides a series of benefits, such as improved
bandwidth, that outweigh the costs in lost gain and increased complexity in amplifier design.
XoXi
Xf
Xs +-
βf
04/19/2023 26 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Feedback Amplifier Analysis
AA
A
X
XA
X
XA
XX
AX
X
XA
bygivenisfeedbackwithgainsamplifierThe
sourcethefromsignaltheX
amplifierbasicthetosignalinputnettheisXwhereXXX
gainvoltagegegainsamplifiertheisAwhereAXX
factorfeedbackthecallediswhereXX
f
i
of
i
ffi
i
s
of
s
ifsi
io
foff
111
'
,
..,'
XoXi
Xf
Xs +-
βf
04/19/2023 27 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Summary: General Feedback Structure
A
Source Load+
-
Vs
Vf
V V A : Open Loop Gain A = Vo / V : feedback factor = Vf / Vo
VAV
VVV
VV
VVV
o
oS
of
fs
1 :Note
1 :feedback ofAmount
:Gain Loop
)1
(1
1 :gain loop Close
Af
s
of
A
A
AT
T
T
A
A
V
VA
The product Aβ must be positive for the feedback network to be the negative feedback network.
04/19/2023 28 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
* Gain desensitivity - less variation in amplifier gain with changes in β (current gain) of transistors due to dc bias, temperature, fabrication process variations, etc.
* Bandwidth extension - extends dominant high and low frequency poles to higher and lower frequencies, respectively.
* Noise reduction - improves signal-to-noise ratio* Improves amplifier linearity - reduces distortion in signal due to gain
variations due to transistors* Impedance Control - control input and output impedances by applying
appropriate feedback topologies
* Cost of these advantages:æ Loss of gain, may require an added gain stage to compensate.æ Added complexity in design
Advantages of Negative Feedback
AAf
LLfHfHf
1
1
04/19/2023 29 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Gain Desensitivity
Feedback can be used to desensitize the closed-loop gain to variations in the basic amplifier. Let’s see how.
Assume β is constant. Taking differentials of the closed-loop gain equation gives…
Divide by Af
This result shows the effects of variations in A on Af is mitigated by the feedback amount. 1+Aβ is also called the desensitivity amount
We will see through examples that feedback also affects the input and resistance of the amplifier (increases Ri and decreases Ro by 1+Aβ factor)
21 AdA
dAf
A
dA
AA
A
A
dA
A
dA
f
f
1
11
1 2
AA
Af
1
04/19/2023 30 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Bandwidth Extension
We’ve mentioned several times in the past that we can trade gain for bandwidth. Finally, we see how to do so with feedback… Consider an amplifier with a high-frequency response characterized by a single pole and the expression: Apply negative feedback β and the resulting closed-loop gain is:
•Notice that the midband gain reduces by (1+AMβ) while the 3-dB roll-off frequency increases by (1+AMβ)
H
M
s
AsA
1
MH
MMf As
AA
sA
sAsA
11
1
1
04/19/2023 31 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Finding Loop Gain
Generally, we can find the loop gain with the following steps:
– Break the feedback loop anywhere (at the output in the ex. below) – Zero out the input signal xs
– Apply a test signal to the input of the feedback circuit – Solve for the resulting signal xo at the output
If xo is a voltage signal, xtst is a voltage and measure the open-circuit voltage
If xo is a current signal, xtst is a current and measure the short-circuit current
– The negative sign comes from the fact that we are apply negative feedback
A
xs=0
xf
xi
xoxtst
Ax
x
AxAxAxx
xx
xx
tst
o
tstfio
fi
tstf
gain loop
0
04/19/2023 32 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
* There are four types of feedback amplifiers. Why?æ Output sampled can be a current or a voltageæ Quantity fed back to input can be a current or a voltageæ Four possible combinations of the type of output sampling and input
feedback* One particular type of amplifier, e.g. voltage amplifier, current amplifier,
etc. is used for each one of the four types of feedback amplifiers. * Feedback factor βf is a different type of quantity, e.g. voltage ratio,
resistance, current ratio or conductance, for each feedback configuration.* Before analyzing the feedback amplifier’s performance, need to start by
recognizing the type or configuration.* Terminology used to name types of feedback amplifier, e.g. Series-shunt
æ First term refers to nature of feedback connection at the input.æ Second term refers to nature of sampling connection at the output.
Basic Types of Feedback Amplifiers
04/19/2023 33 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Basic Feedback Topologies
Depending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used.
(Type of Feedback) (Type of Sensing)
(1) Series (Voltage) Shunt (Voltage)
(2) Series (Voltage) Series (Current)
(3) Shunt (Current) Shunt (Voltage)
(4) Shunt (Current) Series (Current)
EIE 211 Electronic Devices and Circuit Design II
Figure 8.4 The four basic feedback topologies: (a) voltage-mixing voltage-sampling (series–shunt) topology; (b) current-mixing current-sampling (shunt–series) topology; (c) voltage-mixing current-sampling (series–series) topology; (d) current-mixing voltage-sampling (shunt–shunt) topology.
EIE 211 Electronic Devices and Circuit Design II
Basic Feedback Topologies
Depending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used (series-shunt, series-series, shunt-shunt, or shunt-series)
Voltage amplifier – voltage-controlled voltage source Requires high input impedance, low output impedance Use series-shunt feedback (voltage-voltage feedback)
Current amplifier – current-controlled current source Use shunt-series feedback (current-current feedback)
Transconductance amplifier – voltage-controlled current source Use series-series feedback (current-voltage feedback)
Transimpedance amplifier – current-controlled voltage source Use shunt-shunt feedback (voltage-current feedback)
series-shunt
shunt-series
series-series
shunt-shunt
04/19/2023 36
EIE 211 Electronic Devices and Circuit Design II
Series-Shunt Feedback Amplifier - Ideal Case* Assumes feedback circuit does not load down the basic
amplifier A, i.e. doesn’t change its characteristics® Doesn’t change gain A® Doesn’t change pole frequencies of basic
amplifier A
® Doesn’t change Ri and Ro
* For the feedback amplifier as a whole, feedback does change the midband voltage gain from A to Af
* Does change input resistance from Ri to Rif
* Does change output resistance from Ro to Rof
* Does change low and high frequency 3dB frequencies
A
AA
ff
1
ARR fiif 1
A
RR
f
oof
1
AAf
LLfHfHf
1
1
Basic Amplifier
Feedback Circuit
Equivalent Circuit for Feedback Amplifier
04/19/2023 37 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Series-Shunt Feedback Amplifier - Ideal CaseMidband Gain
Vf
V
i
of
V
i
f
V
fi
iV
s
oVf A
A
V
VA
V
VA
VV
VA
V
VA
111
Input Resistance
Vfi
ii
ofi
i
fi
i
sif AR
RV
VV
I
VV
I
VR
1
Output Resistance
Vt
It
fV
o
t
tof
o
fVt
o
tfVt
o
fVtt
tfoff
fis
o
iVtt
A
R
I
VRso
R
AV
R
VAV
R
VAVI
soVVVand
VVsoVBut
R
VAVI
1
1
0
04/19/2023 38 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Series-Shunt Feedback Amplifier - Ideal Case
of
LLf
of
ofo
Lf
fo
of
L
of
o
ofL
o
L
of
L
o
ff
L
o
AA
AAwhere
s
A
sA
A
A
As
A
s
A
s
A
A
AAthen
s
AAFor
11
11
11
1
1
11
1
11
Low Frequency Pole
High Frequency Pole
ofHHfof
ofo
Hf
fo
ofH
of
o
ofH
o
H
of
H
o
ff
H
o
AA
AAwhere
s
A
A
s
A
A
As
A
sA
sA
A
AAthen
sA
AFor
11
11
1
1
1
11
1
11
Low 3dB frequency lowered by feedback.
Upper 3dB frequency raised by feedback.
04/19/2023 39 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
39
* Feedback networks consist of a set of resistors æ Simplest case (only case considered here)æ In general, can include C’s and L’s (not
considered here)æ Transistors sometimes used (gives variable
amount of feedback) (not considered here)* Feedback network needed to create Vf feedback
signal at input (desirable)
* Feedback network has parasitic (loading) effects including:
* Feedback network loads down amplifier inputæ Adds a finite series resistanceæ Part of input signal Vs lost across this series
resistance (undesirable), so Vi reduced
* Feedback network loads down amplifier outputæ Adds a finite shunt resistanceæ Part of output current lost through this shunt
resistance so not all output current delivered to load RL (undesirable)
Practical Feedback Networks
Vi
Vf
Vo
* How do we take these loading effects into account?
04/19/2023 40 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
* Need to find an equivalent network for the feedback network including feedback effect and loading effects.
* Feedback network is a two port network (input and output ports)
* Can represent with h-parameter network (This is the best for this particular feedback amplifier configuration)
* h-parameter equivalent network has FOUR parameters
* h-parameters relate input and output currents and voltages
* Two parameters chosen as independent variables. For h-parameter network, these are input current I1 and output voltage V2
* Two equations relate other two quantities (output current I2 and input voltage V1) to these independent variables
* Knowing I1 and V2, can calculate I2 and V1 if you know the h-parameter values
* h-parameters can have units of ohms, 1/ohms or no units (depends on which parameter)
Equivalent Network for Feedback Network
04/19/2023 41 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
* Feedback network consists of a set of resistors* These resistors have loading effects on the basic
amplifier, i.e they change its characteristics, such as the gain
* Can use h-parameter equivalent circuit for feedback network æ Feedback factor βf given by h12 since
æ Feedforward factor given by h21 (neglected)
æ h22 gives feedback network loading on output
æ h11 gives feedback network loading on input
* Can incorporate loading effects in a modified basic amplifier. Basic gain of amplifier AV becomes a new, modified gain AV’ (incorporates loading effects).
* Can then use feedback analysis from the ideal case.
Series-Shunt Feedback Amplifier - Practical Case
fo
f
IV
V
V
Vh
02
112
1
'1
'1
'1'1
'1
'
Vf
LLfHVfHf
fV
oofVfiif
Vf
VVf
AA
A
RRARR
A
AA
sifin RRR )11
/(1Lof
out RRR
04/19/2023 42
EIE 211 Electronic Devices and Circuit Design IISeries-Shunt Feedback Amplifier - Practical Case
* How do we determine the h-parameters for the feedback network?
* For the input loading term h11 æ Turn off the feedback signal by
setting Vo = 0.æ Then evaluate the resistance seen
looking into port 1 of the feedback network (also called R11 here).
* For the output loading term h22
æ Open circuit the connection to the input so I1 = 0.
æ Find the resistance seen looking into port 2 of the feedback network (also called R22 here).
* To obtain the feedback factor βf (also called h12 )æ Apply a test signal Vo’ to port 2 of the
feedback network and evaluate the feedback voltage Vf (also called V1 here) for I1 = 0.
æ Find βf from βf = Vf/Vo’
Summary of Feedback Network Analysis
04/19/2023 43 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
* Evaluate modified basic amplifier (including loading effects of feedback network)æ Including h11 at inputæ Including h22 at outputæ Including loading effects of source resistanceæ Including load effects of load resistance
* Analyze effects of idealized feedback network using feedback amplifier equations derived
* Note æ Av’ is the modified voltage gain including the
effects of h11 , h22 , RS and RL. æ Ri’, Ro’ are the modified input and output
resistances including the effects of h11 , h22 , RS and RL.
Summary of Approach to Analysis
'1
'1
'1
''1'
'1
'
Vf
LLfHVfHf
fV
oofVfiif
Vf
VVf
AA
A
RRARR
A
AA
Modified Basic Amplifier
Idealized Feedback Network
Practical Feedback Network
Basic Amplifier
04/19/2023 44 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
Example: Find expression for A, β, the closed-loop gain Vo/Vs, the input resistance Rin, and the output resistance Rout. Given μ = 104, Rid =100 kΩ, Ro = 1 kΩ, RL = 2 kΩ, R1 = 1 kΩ, R2 = 1MΩ and Rs = 10 kΩ.
04/19/2023 45 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II
04/19/2023 46 King Mongkut’s University of Technology Thonburi
EIE 211 Electronic Devices and Circuit Design II