SCDA060 Application note

SCDA060 May 2025 CD4053B

3.1 Pull-down Resistor

A pull-down resistor R1 can be connected to the output as shown in Figure 3-2.

Figure 3-2 Pull-down Resistor

A trade-off exists in the selection of R1.

R1 needs to be chosen far more less than the input resistance of op amp and the OFF resistance of CD4053B to make sure the voltage across is nearly zero.

Equation (3) can be used to prove this. Assuming VSS = 0, in this case, V_X = 0, R_X = R1 ∥ R_in,amp, where R_in,amp is the input resistance of unity gain buffer. Then Equation 3 can be rewritten as:

Equation 4.

\frac{V_{D D} - V_{O U T}}{R_{o f f, u p}} - \frac{V_{O U T}}{R_{o f f, d o w n}} = \frac{V_{O U T}}{R 1 ∥ R_{i n, a m p}}

Equation 5.

V_{O U T} = V_{D D} \frac{R_{o f f, d o w n} ∥ R 1 ∥ R_{i n, a m p}}{R_{o f f, d o w n} ∥ R 1 ∥ R_{i n, a m p} + R_{o f f, u p}}

If R1 ≪ R_off,up, R_off,down, R_in,amp, the item R_off,down ∥ R1 ∥ R_in,amp ≈ R1, and:

Equation 6.

V_{O U T} \approx V_{D D} \frac{R_{1}}{R_{1} + R_{o f f, u p}} = V_{D D} \frac{1}{1 + \frac{R_{o f f, u p}}{R_{1}}} \approx 0

To validate Equation 6, R1 must be at least smaller than R_off,up, R_off,down and R_in,amp. The following paragraphs use the data sheet of op amp and multiplexer to calculate these values.

R_in,amp is usually calculated with common-mode voltage and input bias current:

Equation 7.

R_{i n, a m p} = \frac{∆ V_{C M}}{∆ I_{B}}

The relationship between common-mode voltage and input bias current is given in the data sheet. Take TLV9004 as an example:

Figure 3-3 I_B and I_OS vs Common-Mode Voltage

∆V_CM = 5.5V, ∆I_B ≈ 0.9pA, and R_in,amp is calculated to be 6.1TΩ. Therefore, R1 must be less than 610GΩ.

The off resistance R_off,up can be calculated by Equation 1.

For CD4053B:

The typical value of I_OFF mentioned in the data sheet is 0.3nA (with VDD = 18V, VEE = VSS = 0, ambient temperature = 25℃). Then R_off,up is calculated to be 60GΩ.
The largest value of is 1000nA (with VDD = 18V, VEE = VSS = 0, ambient temperature = 85 ℃). Then R_off,up is calculated to be 18MΩ.

Using the typical value of I_OFF to calculate, R1 needs to be less than 6GΩ. Using the largest value of I_OFF to calculate, R1 needs to be less than 1.8MΩ.

To choose the appropriate R1 value, three considerations are made here:

Less than 6GΩ is possibly not applied to every situation, because the typical value of I_OFF does not take the temperature variation into account.
Less than 1.8MΩ can be an overestimation, since the largest value of I_OFF also applies to CD4051B, which is a sum of 8 channels’ leakage.
Too large value of R1 in the layout can make the circuit vulnerable to noise and interference.

To be more reliable, R1 is recommended to be no more than 1MΩ.

Also, R1 needs to be large enough so that when the channel is turned ON, the voltage on R1 is almost equal to the input voltage. Figure 3-4 models the effect of R1 on the signal transmission when the channel is ON.

Figure 3-4 Pull-down Resistor’s Effect When Channel Is ON

Assuming VSS = 0, V_OUT can be written as:

Equation 8.

V_{O U T} = V_{I N} \frac{R_{1} ∥ R_{i n, a m p}}{R_{1} ∥ R_{i n, a m p} + R_{O N}}

Since R1 is usually quite small compared to the input resistance of op amp,

Equation 9.

V_{O U T} \approx V_{I N} \frac{R_{1}}{R_{1} + R_{O N}}

As can be seen from the previous equation, V_OUT is smaller than V_IN, and this effect needs to not be neglected when R1 is not large enough. The recommendation is that R1 needs to be at least 10 times of R_ON to avoid too much degradation of input signal.

For CD4053B, the largest value of R_ON mentioned in the data sheet is 1300Ω (with VDD = 5V, VEE = VSS = 0, ambient temperature = 125℃). Hence, at least 10kΩ is required for R1.

To sum up, the recommended value of R1 is 10kΩ to approximately 1MΩ.