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☀ מצב בהיר
2.1
▾
✕
V
in
= V
+
− V
−
V
out
= A
V
·V
in
A
V
→ ∞
0.00 mV
0.00 mV
V
V
0.00 mV
0.0 V
0.00 V
V
in
= V⁺ − V⁻ = 1.2 − (−0.4) = +1.6 mV
A
V
·V
in
≈ 200000 · 0.0016 = 320 V ≫ V
cc
V
in
> 0 ⟹ V
out
= +V
cc
= +9 V
2.2
▾
✕
A
v
=
V
out
V
in
= 1 +
R
2
R
1
V⁺ = V⁻
i⁺ = i⁻ = 0
3.0 V
kΩ
kΩ
V
V
—
—
—
—
V⁻ = V⁺ = 3 V
i₁ =
V⁻
R1
=
3 V
5 kΩ
= 0.6 mA
i₂ = i₁ = 0.6 mA
Vout = V⁻ + i₂·R2 = 3 + 0.6mA·15kΩ = 3 + 9 = 12 V
A
v
= 1 +
R2
R1
= 1 +
15 kΩ
5 kΩ
= 4 → V
out
= 4 · 3 V = 12 V ✓
2.3
▾
✕
A
v
=
V
out
V
in
= −
R
f
R
1
1.0 V
kΩ
kΩ
V
V
—
—
—
—
V⁻ = V⁺ = 0 V
i =
V
in
− V⁻
R
1
=
0.5 V
2 kΩ
= 0.25 mA
V
out
= V⁻ − i·R
f
= 0 − 0.25 mA · 18 kΩ = −4.5 V
A
v
=
−4.5 V
0.5 V
= −9 ✓ −
18 kΩ
2 kΩ
= −9
−9 · 2 V = −18 V → |−18| > 12 → V
out
= −12 V
2.4
▾
✕
V
out
= V
in
A
v
= 1
R
in
→ ∞
R
out
→ 0
2.0 V
kΩ
kΩ
V
V
—
—
—
—
i =
V
s
R
s
+ R
L
=
2 V
9 kΩ + 1 kΩ
= 0.2 mA
V
L
= i · R
L
= 0.2 mA · 1 kΩ = 0.2 V
i
s
= 0 → V⁺ = 2 V → V
L
= V
out
= 2 V
i
L
=
V
L
R
L
=
2 V
1 kΩ
= 2 mA
2.5
▾
✕
V
out
= − R
f
· (
V
1
R
1
+
V
2
R
2
+
V
3
R
3
+ … )
R
1
= R
2
= … = R
f
⟹ V
out
= −(V
1
+ V
2
+ V
3
+ …)
kΩ
V
V
—
—
—
V⁻ = V⁺ = 0 V
i
1
=
2 V
10 kΩ
= 0.2 mA
i
2
=
3 V
20 kΩ
= 0.15 mA
i
3
=
−1 V
5 kΩ
= −0.2 mA
i
f
= i
1
+ i
2
+ i
3
= 0.2 + 0.15 − 0.2 = 0.15 mA
V
out
= 0 − i
f
· R
f
= −0.15 mA · 10 kΩ = −1.5 V
V
out
= −10 · (
2
10
+
3
20
+
−1
5
) = −10 · 0.15 = −1.5 V ✓
2.6
▾
✕
V
+
=
V
1
R
1
+
V
2
R
2
+ …
1
R
1
+
1
R
2
+ …
V
out
= ( 1 +
R
f
R
g
) · V
+
R
1
= R
2
= … = R
n
⟹ V
+
=
V
1
+ V
2
+ … + V
n
n
1 +
R
f
R
g
= n ⟹ V
out
= V
1
+ V
2
+ … + V
n
kΩ
kΩ
V
V
—
—
—
—
V
+
=
2
10
+
4
10
1
10
+
1
10
=
0.6
0.2
= 3 V
i
1
=
2 − 3
10 kΩ
= −0.1 mA
i
2
=
4 − 3
10 kΩ
= 0.1 mA
A
v
= 1 +
R
f
R
g
= 1 +
10
10
= 2
V
out
= 2 · 3 = 6 V = V
1
+ V
2
✓
i
f
=
6 − 3
10 kΩ
=
3
10 kΩ
= 0.3 mA ✓
2.7
▾
✕
V
out
= −
R
f
R
1
· V
1
+ ( 1 +
R
f
R
1
) ·
R
3
R
2
+ R
3
· V
2
R
1
= R
2
, R
f
= R
3
⟹ V
out
=
R
f
R
1
· ( V
2
− V
1
)
kΩ
kΩ
V
V
—
—
—
—
V
+
= V
2
·
R
3
R
2
+ R
3
= 6 ·
20
30
= 4 V
i
2
=
6 V
30 kΩ
= 0.2 mA
V
−
= V
+
= 4 V
i
1
=
V
1
− V
−
R
1
=
2 − 4
10 kΩ
= −0.2 mA
V
out
= V
−
− i
1
· R
f
= 4 − (−0.2 mA) · 20 kΩ = 8 V
V
out
=
20
10
· (6 − 2) = 2 · 4 = 8 V ✓
2.8
▾
✕
0.01
log = −2
0.1
log = −1
1
log = 0
2
log ≈ 0.3
10
log = 1
100
log = 2
1000
log = 3
1,000,000
log = 6
log x =
—
20 · log x =
—
A
v
[dB] = 20 · log (
V
out
V
in
)
A
p
[dB] = 10 · log (
P
out
P
in
)
A = A
1
· A
2
· A
3
⟹ A[dB] = A
1
[dB] + A
2
[dB] + A
3
[dB]
×0.1
−20 dB
×0.5
−6 dB
×0.707
−3 dB
×1
0 dB
×1.414
+3 dB
×2
+6 dB
×10
+20 dB
×100
+40 dB
×1000
+60 dB
V
V
—
—
—
—
A
1
= 1 +
9
1
= 10
A
1
[dB] = 20 · log 10 = 20 dB
A
2
= −
20
10
= −2
A
2
[dB] = 20 · log 2 = 6.02 dB
A = 10 · (−2) = −20
A[dB] = 20 + 6.02 = 26.02 dB = 20 · log 20 ✓
V
out
= −20 · 50 mV = −1 V
2.9
▾
✕
V
TH
= +V
sat
·
R
1
R
1
+ R
2
V
TL
= −V
sat
·
R
1
R
1
+ R
2
V
TH
= +V
sat
·
R
1
R
2
V
TL
= −V
sat
·
R
1
R
2
ΔV = V
TH
− V
TL
kΩ
kΩ
V
V
V
—
—
—
—
V
TH
= 12 ·
10
10 + 20
= 4 V
V
TL
= −12 ·
10
10 + 20
= −4 V
ΔV = 4 − (−4) = 8 V
i =
12 V
30 kΩ
= 0.4 mA
V
in
↑ 4 V ⟹ V
out
= −12 V
V
in
↓ −4 V ⟹ V
out
= +12 V
→
🏠
♿