Chapter 16, Problem 16.36P

(a)

To determine

To plot: The graph of current in the transistor as a function of the input voltage for given range.

Answer to Problem 16.36P

The required plot is shown in Figure 2

Explanation of Solution

Calculation:

The given diagram is shown in Figure 1.

  

Consider the case when the input voltage is equal to zero.

The NMOS device is in the cutoff region the drain current of the transistor is zero and when the PMOS transistor is in the non-saturation region its drain current is also zero.

Consider the case when $0\le v_I\le \frac{V_{DD}}{2}$ .

The PMOS transistor in the Non-saturation and the NMOS just started to conduct and then enter in the saturation mode.

The expression for the drain current of the NMOS transistor is given by,

  $i_{DN}=K_N{\left(v_I-V_{TN}\right)}^2$

The expression for the drain current of the PMOS transistor is given by,

  $i_{DP}=K_P{\left(v_I-V_{TN}\right)}^2$

The CMOS drain current is due to the drain current of the NMOS alone and is given by,

  $i_D=i_{DN}$

Substitute $K_N{\left(v_I-V_{TN}\right)}^2$ for $i_{DN}$ in the above equation.

  $i_D=K_N{\left(v_I-V_{TN}\right)}^2$

Substitute $120\text{μA}/{\text{V}}^2$ for $K_N$ and $0.4\text{V}$ for $V_{TN}$ in the above equation.

  $i_D=120\text{μA}/{\text{V}}^2{\left(v_I-0.4\text{V}\right)}^2$

The tale to determine the value of the output current for the different value of the output voltage is shown below.

The required table is shown in Table 1

Table 1

$v_I\left(\text{V}\right)$	$i_D\left(\text{μA}\right)\text{A}$
$0.5$	$1.26$
$0.6$	$5.04$
$0.8$	$20.1$
$0.9$	$31.5$
$1.1$	$61.74$
$1.25$	$91.25$

Consider the case when the input voltage is $\frac{V_{DD}}{2}\le v_I\ge V_{DD}+V_{TP}$ , in this case the NMOS is in non-saturation and the PMOS is in saturation.

The expression for the drain current of the PMOS in saturation is given by,

  $i_{DP}=K_P{\left(V_{DD}-v_I+V_{TP}\right)}^2$

The expression for the drain current of the NMOS in non-saturation is given by,

  $i_{DN}=K_N\left(2\left(v_I-V_{TN}\right)v_O-{\left(v_O\right)}^2\right)$

The CMOS current depends only on the current through the drain current of the PMOS and is given by,

  $i_D=i_{DP}$

Substitute $K_P{\left(V_{DD}-v_I+V_{TP}\right)}^2$ for $i_{DP}$ in the above equation.

  $i_D=K_P{\left(V_{DD}-v_I+V_{TP}\right)}^2$

Substitute $2.5\text{V}$ for $V_{DD}$ , $120\text{μA}/{\text{V}}^2$ for $K_N$ and $-0.6\text{V}$ for $V_{TP}$ in the above equation.

  $i_D=120\text{μA}/{\text{V}}^2{\left(2.5\text{V}+6.63\times {10}^{-34}\text{J}\cdot \text{s}{v}_I-0.6\text{V}\right)}^2$

The table for the output current for the different values of the input voltage is shown below.

The required table is shown in Table 2

Table 2

$v_I\left(\text{V}\right)$	$i_D\left(\text{μA}\right)\text{A}$
$1.3$	$43.2$
$1.4$	$30$
$1.5$	$25$
$1.6$	$10$
$1.8$	$1.2$
$1.9$	$0$

Consider the case when the input voltage is given by,

  $V_{DD}+V_{TP}\le v_I\ge V_{DD}$

For the above case the NMOS is in non-saturation region and the drain current is zero. The PMOS is in cut off and the drain current zero as the circuit is open.

The drain current when the input voltage is zero and the circuit is opened is given by,

  $i_D=0$

The plot for the CMOS drain current against the input voltage from the values of table 1 and table 2 is shown below.

The required plot is shown in Figure 2

  

Conclusion:

Therefore, the required plot is shown in Figure 2.

(b)

To determine

To plot: The current in the transistor as a function fo the input voltage.

Answer to Problem 16.36P

The required plot is shown in Figure 3

Explanation of Solution

Calculation:

Consider the case when the voltage $V_{DD}$ is $1.8\text{V}$ .

Consider the input voltage as $0\le v_I\ge V_{TN}$ , for this case the NMOS is in cutoff the drain current is zero for both the transistor, thus the PMOS is in non-saturation.

Consider the case when the input voltage is $V_{TN}\le v_I\le \frac{V_{DD}}{2}$ .

The expression for the drain current of the NMOS is given by,

  $i_{DN}=K_N{\left(v_I-V_{TN}\right)}^2$

The expression for the drain current of the PMOS transistor is given by,

  $i_{DP}=K_P\left(2\left(V_{DD}-v_I+V_{TP}\right)\left(V_{DD}-v_O\right)-{\left(V_{DD}-v_O\right)}^2\right)$

The CMOS drain current is due to the drain current of the NMOS alone and is given by,

  $i_D=i_{DN}$

Substitute $K_N{\left(v_I-V_{TN}\right)}^2$ for $i_{DN}$ in the above equation.

  $i_D=K_N{\left(v_I-V_{TN}\right)}^2$

Substitute $120\text{μA}/{\text{V}}^2$ for $K_N$ and $0.4\text{V}$ for $V_{TN}$ in the above equation.

  $i_D=120\text{μA}/{\text{V}}^2{\left(v_I-0.4\text{V}\right)}^2$

The table for the output current for the different values of the input voltage is shown below.

The required table is shown in Table 3

Table 3

$v_I\left(\text{V}\right)$	$i_D\left(\text{μA}\right)\text{A}$
$0.5$	$1.26$
$0.6$	$5.04$
$0.8$	$20.1$
$0.9$	$31.5$

Consider the case when the input voltage $v_I$ is $\frac{V_{DD}}{2}<v_I>V_{DD}+V_{TP}$ .

The PMOS transistor is in the non-saturation and the NMOS just beings to conduct and then goes to saturation.

The expression for the drain current of the NMOS is given by,

  $i_{DN}=K_N{\left(2\left(v_I-V_{TN}\right)v_O-v_O^2\right)}^2$

The expression for the drain current of the PMOS transistor is given by,

  $i_{DP}=K_P{\left(V_{DD}-v_I+V_{TP}\right)}^2$

The CMOS drain current is due to the drain current of the PMOS alone and is given by,

  $i_D=i_{DP}$

Substitute $K_P{\left(V_{DD}-v_I+V_{TP}\right)}^2$ for $i_{DP}$ in the above equation.

  $i_D=K_P{\left(V_{DD}-v_I+V_{TP}\right)}^2$

Substitute $1.8\text{V}$ for $V_{DD}$ , $120\text{μA}/{\text{V}}^2$ for $K_P$ and $-0.6\text{V}$ for $V_{TN}$ in the above equation.

  $i_D=120\text{μA}/{\text{V}}^2{\left(1.8\text{V}-v_I-0.6\text{V}\right)}^2$

The table for the output current for the different values of the input voltage is shown below.

The required table is shown in Table 4

Table 4

$v_I\left(\text{V}\right)$	$i_D\left(\text{μA}\right)\text{A}$
$0.95$	$7.5$
$1$	$4.8$
$1.1$	$1.2$
$1.2$	$0$

Consider the case when the input voltage is $V_{DD}+V_{TP}\le v_I>V_{DD}$ the NMOS is in non-saturation, and the value of the drain current is zero, the PMOS is in cut off. Thus, the drain current of the CMOS is in cut off and the circuit is opened.

The plot between the drain current and the input voltage from table 3 and table 4 is shown below.

The required plot is shown in Figure 3

  

Conclusion:

Therefore, the required plot is shown in Figure 3