The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

Question

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Answer 1

Question

Chapter 11, Problem 11.80P

(a)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(a)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 1

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.25 mA=0.25 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.25 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.25 mA=248.344 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=248.344 μA0.026 V=9.5517 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm2$

Substitute $150$ for $β$ and $9.5517 mA/V$ for $gm$ in the above equation.

$rπ2=1509.5517 mA/V=15.7 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−248.344 μA=251.66 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $251.66 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(251.66 μA)=448.69 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $448.69 μA/V$ for $gm1$ , $9.5517 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=448.69 μA/V(1+(9.5517 mA/V)(15.7 kΩ))1+(448.69 μA/V)15.7 kΩ=8.416 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

(b)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(b)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 2

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.05 mA=0.45 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.45 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.45 mA=447.02 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=447.02 μA0.026 V=17.193 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm$

Substitute $150$ for $β$ and $17.193 mA/V$ for $gm2$ in the above equation.

$rπ2=15017.193 mA/V=8.724 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−447.02 μA=52.98 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $52.98 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(52.98 μA)=205.87 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $205.87 μA/V$ for $gm1$ , $17.193 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=205.87 μA/V(1+(17.193 mA/V)(8.724 kΩ))1+(205.87 μA/V)15.7 kΩ=0.0312.796=11.087 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

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Answer 2

Question

Chapter 11, Problem 11.80P

(a)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(a)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 1

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.25 mA=0.25 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.25 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.25 mA=248.344 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=248.344 μA0.026 V=9.5517 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm2$

Substitute $150$ for $β$ and $9.5517 mA/V$ for $gm$ in the above equation.

$rπ2=1509.5517 mA/V=15.7 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−248.344 μA=251.66 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $251.66 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(251.66 μA)=448.69 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $448.69 μA/V$ for $gm1$ , $9.5517 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=448.69 μA/V(1+(9.5517 mA/V)(15.7 kΩ))1+(448.69 μA/V)15.7 kΩ=8.416 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

(b)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(b)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 2

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.05 mA=0.45 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.45 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.45 mA=447.02 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=447.02 μA0.026 V=17.193 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm$

Substitute $150$ for $β$ and $17.193 mA/V$ for $gm2$ in the above equation.

$rπ2=15017.193 mA/V=8.724 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−447.02 μA=52.98 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $52.98 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(52.98 μA)=205.87 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $205.87 μA/V$ for $gm1$ , $17.193 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=205.87 μA/V(1+(17.193 mA/V)(8.724 kΩ))1+(205.87 μA/V)15.7 kΩ=0.0312.796=11.087 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

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Answer 3

Question

Chapter 11, Problem 11.80P

(a)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(a)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 1

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.25 mA=0.25 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.25 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.25 mA=248.344 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=248.344 μA0.026 V=9.5517 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm2$

Substitute $150$ for $β$ and $9.5517 mA/V$ for $gm$ in the above equation.

$rπ2=1509.5517 mA/V=15.7 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−248.344 μA=251.66 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $251.66 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(251.66 μA)=448.69 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $448.69 μA/V$ for $gm1$ , $9.5517 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=448.69 μA/V(1+(9.5517 mA/V)(15.7 kΩ))1+(448.69 μA/V)15.7 kΩ=8.416 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

(b)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(b)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 2

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.05 mA=0.45 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.45 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.45 mA=447.02 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=447.02 μA0.026 V=17.193 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm$

Substitute $150$ for $β$ and $17.193 mA/V$ for $gm2$ in the above equation.

$rπ2=15017.193 mA/V=8.724 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−447.02 μA=52.98 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $52.98 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(52.98 μA)=205.87 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $205.87 μA/V$ for $gm1$ , $17.193 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=205.87 μA/V(1+(17.193 mA/V)(8.724 kΩ))1+(205.87 μA/V)15.7 kΩ=0.0312.796=11.087 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

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Answer 4

Question

Chapter 11, Problem 11.80P

(a)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(a)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 1

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.25 mA=0.25 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.25 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.25 mA=248.344 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=248.344 μA0.026 V=9.5517 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm2$

Substitute $150$ for $β$ and $9.5517 mA/V$ for $gm$ in the above equation.

$rπ2=1509.5517 mA/V=15.7 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−248.344 μA=251.66 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $251.66 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(251.66 μA)=448.69 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $448.69 μA/V$ for $gm1$ , $9.5517 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=448.69 μA/V(1+(9.5517 mA/V)(15.7 kΩ))1+(448.69 μA/V)15.7 kΩ=8.416 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

(b)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(b)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 2

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.05 mA=0.45 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.45 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.45 mA=447.02 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=447.02 μA0.026 V=17.193 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm$

Substitute $150$ for $β$ and $17.193 mA/V$ for $gm2$ in the above equation.

$rπ2=15017.193 mA/V=8.724 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−447.02 μA=52.98 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $52.98 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(52.98 μA)=205.87 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $205.87 μA/V$ for $gm1$ , $17.193 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=205.87 μA/V(1+(17.193 mA/V)(8.724 kΩ))1+(205.87 μA/V)15.7 kΩ=0.0312.796=11.087 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

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Answer 5

Chapter 11, Problem 11.80P

(a)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(a)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 1

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.25 mA=0.25 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.25 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.25 mA=248.344 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=248.344 μA0.026 V=9.5517 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm2$

Substitute $150$ for $β$ and $9.5517 mA/V$ for $gm$ in the above equation.

$rπ2=1509.5517 mA/V=15.7 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−248.344 μA=251.66 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $251.66 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(251.66 μA)=448.69 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $448.69 μA/V$ for $gm1$ , $9.5517 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=448.69 μA/V(1+(9.5517 mA/V)(15.7 kΩ))1+(448.69 μA/V)15.7 kΩ=8.416 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

(b)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(b)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 2

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.05 mA=0.45 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.45 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.45 mA=447.02 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=447.02 μA0.026 V=17.193 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm$

Substitute $150$ for $β$ and $17.193 mA/V$ for $gm2$ in the above equation.

$rπ2=15017.193 mA/V=8.724 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−447.02 μA=52.98 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $52.98 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(52.98 μA)=205.87 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $205.87 μA/V$ for $gm1$ , $17.193 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=205.87 μA/V(1+(17.193 mA/V)(8.724 kΩ))1+(205.87 μA/V)15.7 kΩ=0.0312.796=11.087 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Answer 6

Chapter 11, Problem 11.80P

(a)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(a)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 1

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.25 mA=0.25 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.25 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.25 mA=248.344 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=248.344 μA0.026 V=9.5517 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm2$

Substitute $150$ for $β$ and $9.5517 mA/V$ for $gm$ in the above equation.

$rπ2=1509.5517 mA/V=15.7 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−248.344 μA=251.66 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $251.66 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(251.66 μA)=448.69 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $448.69 μA/V$ for $gm1$ , $9.5517 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=448.69 μA/V(1+(9.5517 mA/V)(15.7 kΩ))1+(448.69 μA/V)15.7 kΩ=8.416 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Answer 7

Chapter 11, Problem 11.80P

(a)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

Answer 8

(a)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 1

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.25 mA=0.25 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.25 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.25 mA=248.344 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=248.344 μA0.026 V=9.5517 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm2$

Substitute $150$ for $β$ and $9.5517 mA/V$ for $gm$ in the above equation.

$rπ2=1509.5517 mA/V=15.7 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−248.344 μA=251.66 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $251.66 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(251.66 μA)=448.69 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $448.69 μA/V$ for $gm1$ , $9.5517 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=448.69 μA/V(1+(9.5517 mA/V)(15.7 kΩ))1+(448.69 μA/V)15.7 kΩ=8.416 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=9.5517 mA/V$ , $rπ2=15.7 kΩ$ , $gm1=448.69 μA/V$ and the value of the composite transconductance is $gmC=8.416 mA/V$ .

Answer 13

(b)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

(b)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 2

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.05 mA=0.45 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.45 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.45 mA=447.02 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=447.02 μA0.026 V=17.193 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm$

Substitute $150$ for $β$ and $17.193 mA/V$ for $gm2$ in the above equation.

$rπ2=15017.193 mA/V=8.724 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−447.02 μA=52.98 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $52.98 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(52.98 μA)=205.87 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $205.87 μA/V$ for $gm1$ , $17.193 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=205.87 μA/V(1+(17.193 mA/V)(8.724 kΩ))1+(205.87 μA/V)15.7 kΩ=0.0312.796=11.087 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Answer 14

(b)

To determine

The small signal parameters for each of the transistor and the value of the composite transconductance for the given specifications.

Answer 15

(b)

Expert Solution

Answer to Problem 11.80P

The value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

The given diagram is shown in Figure 1

Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.80P , additional homework tip 2

Figure 1

Calculation:

The expression to determine the value of the emitter current of the second transistor is calculated as,

$IE2=IBias2−IBias1=0.50 mA−0.05 mA=0.45 mA$

The expression to determine the value of the current $IC2$ is given by,

$IC2=(β1+β)IE2$

Substitute $150$ for $β$ and $0.45 mA$ for $IE2$ in the above equation.

$IC2=(1501+150)0.45 mA=447.02 μA$

The value of the transconductance $gm2$ is calculated as,

$gm2=IC20.026 V=447.02 μA0.026 V=17.193 mA/V$

The expression to determine the value of the small signal resistance is given by,

$rπ2=βgm$

Substitute $150$ for $β$ and $17.193 mA/V$ for $gm2$ in the above equation.

$rπ2=15017.193 mA/V=8.724 kΩ$

The value of the drain current $ID1$ is given by,

$ID1=IBias2−IC2=0.50 mA−447.02 μA=52.98 μA$

The value of the transconductance $gm1$ is given by,

$gm1=2KnID1$

Substitute $0.2 mA/V2$ for $kn$ and $52.98 μA$ for $ID1$ in the above equation.

$gm1=2(0.2 mA/V2)(52.98 μA)=205.87 μA/V$

The expression to determine the value of the composite transconductance is given by,

$gmC=gm1(1+gm2rπ)1+gm1rπ$

Substitute $205.87 μA/V$ for $gm1$ , $17.193 mA/V$ for $gm2$ and $15.7 kΩ$ for $rπ$ in the above equation.

$gmC=205.87 μA/V(1+(17.193 mA/V)(8.724 kΩ))1+(205.87 μA/V)15.7 kΩ=0.0312.796=11.087 mA/V$

Conclusion:

Therefore, the value of the small signal parameters are $gm2=17.193 mA/V$ , $rπ2=8.724 kΩ$ , $gm1=205.87 μA/V$ and the value of the composite transconductance is $gmC=11.087 mA/V$ .