# HMC1010　Log slope and intercept calculation formulas

Hi,

My customers are considering HMC 1010.

I got a question about calculation formula of log slope and interception.

If we use RFBK = 4.7 KΩ, RSHUNT = 2.2 KΩ, and RSET = 24 KΩ when determining β on page 11-22, the calculation result is β = 3.33.
However, it is β = 1.67 in the data sheet.

Where did 1/2 come from?

The HMC 1020 data sheet has the same circuit diagram.
However, the formula for determining β = 1/2 (RFBK / (RFBK // RSHUNT // RSET)))).
Is the formula in HMC 1010 data sheet wrong?

Best regards,

Yuya

## Top Replies

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• Hello Yuya,

Standard demo board uses RFBK= RSHUNT= 4.7k. This means output amp Gain= 2. In this standard configuration, slope= 37.3 mV/dB.

Changing RSHUNT= 2.2k and RSET= 24k will increase the slope. Now output amp Gain= 3.3322.

When reconfiguring the demo board for more or less output amplifier gain (or slope), Beta is the ratio of gain increase or decrease. In this example, Beta= 3.3322/2= 1.666. This means Optimized slope= 1.666 * 37.3 = 62 mV/dB, as stated in datasheet.

The generalized formula for Beta is:   Beta= ((RSHUNT || RSET) + RFBK) / 2 (RSHUNT || RSET). The factor of 2 comes from Beta being a relative term (the unmodified demo board output amplifier Gain = 2). It seems that both datasheets have the wrong formula for Beta.

Hope that helps.

• After looking at this again, it seems the datasheet formula vs. the formula above are apparently different but equivalent algebraic expressions for Beta. Therefore, the datasheets are correct, except for the missing factor of 2 in the denominator of HMC1010 datasheet page 21.

Hope that further helps.

Reply
• After looking at this again, it seems the datasheet formula vs. the formula above are apparently different but equivalent algebraic expressions for Beta. Therefore, the datasheets are correct, except for the missing factor of 2 in the denominator of HMC1010 datasheet page 21.

Hope that further helps.

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